Skip to main content
SpringerLink
Log in
Book cover

Classical and Quantum Cosmology pp 153–259Cite as

Inflation

  • Chapter
  • First Online:

  • 2588 Accesses

Part of the book series: Graduate Texts in Physics ((GTP))

Abstract

The hot big bang model is based upon some fundamental assumptions:

  1. (i)

    The laws of physics verified today were valid also in primordial epochs.

  2. (ii)

    The cosmological principle holds.

  3. (iii)

    The initial conditions of the universe at the big bang t bb are such that Ω(t bb) ∼ 1 and the universe is in thermal equilibrium at some temperature T bb > 100 MeV.

  4. (iv)

    Large-scale cosmic structures (CMB anisotropies and galaxy distributions) formed from a primordial spectrum of almost Gaussian density fluctuations.

Le Réel, c’est l’impossible.

— Jacques Lacan, Le Séminaire. Livre XI, XIII.3

The Real is the impossible.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Cosmic strings can give rise to characteristic signatures in the CMB. See, e.g., [23, 24].

  2. 2.

    Here the term “chaotic” loosely refers to the statistical distribution of the initial conditions, not to precise stochastic properties of chaos theory. In Chap. 6, we will see an example of chaotic evolution in the latter mathematical sense.

  3. 3.

    Our definition counts \(\mathcal{N}_{a}\) forward in time, in accordance with [94] where \(\mathcal{N}_{a}(t_{\text{i}}) = 0\) and goes up to \(\mathcal{N}_{a}(t)> 0\). In [95], the “backward” definition is used, where \(\mathcal{N}_{k} =\ln (a_{\text{e}}/a)\) is the number of remaining e-folds at the time t before the end of inflation.

  4. 4.

    Classically, it is sufficient to have a local minimum, but when considering a quantum theory tunneling effects should be taken into account.

  5. 5.

    Extensions of these models include the effect of curvature and a barotropic perfect fluid [121], Bianchi backgrounds [122] and polynomial potentials [123]. The stability of solutions as critical points in phase space was studied for decoupled [120, 124, 125] and coupled [126–128] exponential potentials, for decoupled inverse power-law potentials [125] and for general potentials with or without cross-interactions [129]. Late-time dark-energy scenarios can be found in [125, 130]. Multi-field inhomogeneous perturbations have also been considered at the linear [131] and non-linear level [132–134].

  6. 6.

    A third type of interpretation in quantum cosmology is Bohm interpretation [153].

  7. 7.

    For power-law inflation, the exact expression for \(\mathcal{P}_{\delta \phi }\) is (5.130) with ν ε given again by (5.137) [191].

  8. 8.

    Inflationary non-Gaussianity from self-interaction has been studied extensively in [230–248]. Non-Gaussianities are also generated, for instance, by the inclusion of higher-dimension operators in the inflaton Lagrangian [249], in warm inflation [250, 251], ghost inflation [252, 253] and when assuming that the inflaton does not sit in a vacuum state [186, 187, 254].

  9. 9.

    In [270], various definitions of the second-order curvature perturbation are reviewed.

  10. 10.

    A preheating phase can enhance the tensor signal after inflation, thus enhancing the expectation for detection of a stochastic gravitational-wave background [295].

  11. 11.

    A small non-Gaussian component, proportional to the tensor amplitude and spectral index n t, also comes from the three-point functions involving the graviton zero-mode [245]. Since the tensor amplitude is much smaller than the scalar one, we can neglect this term with respect to the scalar bispectrum.

  12. 12.

    This is due to the fact that, at second order in perturbation theory, the longitudinal gauge condition Φ −Ψ = 0 is modified as Φ (2) −Ψ (2) = 4Ψ 2 at large scales, thus providing a non-trivial second-order correction to the Sachs–Wolfe effect [222].

  13. 13.

    In Polchinski’s formulation [340], a field theory is natural if all masses are forbidden by symmetries. The Standard Model is not natural due to the Higgs mass but, interestingly, this naturalness argument suggests that a new symmetry should appear at electroweak energies.

  14. 14.

    Examples of applications of quantum field theory are the effective field theory approach [341] and the study of inflationary infrared divergences and loop contributions to cosmological observables (see the review [342] and later papers [343–348]).

  15. 15.

    Vector fields have also been considered as curvaton or auxiliary fields [360–366] and in the context of dark energy [367–373].

References

  1. H. Georgi, S.L. Glashow, Unity of all elementary particle forces. Phys. Rev. Lett. 32, 438 (1974)

    Article  ADS  Google Scholar 

  2. H. Georgi, H.R. Quinn, S. Weinberg, Hierarchy of interactions in unified gauge theories. Phys. Rev. Lett. 33, 451 (1974)

    Article  ADS  Google Scholar 

  3. H. Georgi, The state of the art—Gauge theories. AIP Conf. Proc. 23, 575 (1975)

    Article  ADS  Google Scholar 

  4. H. Fritzsch, P. Minkowski, Unified interactions of leptons and hadrons. Ann. Phys. (N.Y.) 93, 193 (1975)

  5. A.J. Buras, J.R. Ellis, M.K. Gaillard, D.V. Nanopoulos, Aspects of the grand unification of strong, weak and electromagnetic interactions. Nucl. Phys. B 135, 66 (1978)

    Article  ADS  Google Scholar 

  6. G. Lazarides, Q. Shafi, C. Wetterich, Proton lifetime and fermion masses in an SO(10) model. Nucl. Phys. B 181, 287 (1981)

    Article  ADS  Google Scholar 

  7. J.R. Ellis, D.V. Nanopoulos, S. Rudaz, A phenomenological comparison of conventional and supersymmetric GUTs. Nucl. Phys. B 202, 43 (1982)

    Article  ADS  Google Scholar 

  8. Y. Hayato et al. [Super-Kamiokande Collaboration], Search for proton decay through \(p \rightarrow \bar{\nu } K^{+}\) in a large water Cherenkov detector. Phys. Rev. Lett. 83, 1529 (1999). [arXiv:hep-ex/9904020]

  9. H. Murayama, A. Pierce, Not even decoupling can save minimal supersymmetric SU(5). Phys. Rev. D 65, 055009 (2002). [arXiv:hep-ph/0108104]

  10. B. Bajc, P. Fileviez Perez, G. Senjanović, Proton decay in minimal supersymmetric SU(5). Phys. Rev. D 66, 075005 (2002). [arXiv:hep-ph/0204311]

  11. K.S. Babu, J.C. Pati, F. Wilczek, Fermion masses, neutrino oscillations, and proton decay in the light of SuperKamiokande. Nucl. Phys. B 566, 33 (2000). [arXiv:hep-ph/9812538]

  12. B. Dutta, Y. Mimura, R.N. Mohapatra, Neutrino mixing predictions of a minimal SO(10) model with suppressed proton decay. Phys. Rev. D 72, 075009 (2005). [arXiv:hep-ph/0507319]

  13. S. Dimopoulos, H. Georgi, Softly broken supersymmetry and SU(5). Nucl. Phys. B 193, 150 (1981)

    Article  ADS  Google Scholar 

  14. S. Dimopoulos, S. Raby, F. Wilczek, Supersymmetry and the scale of unification. Phys. Rev. D 24, 1681 (1981)

    Article  ADS  Google Scholar 

  15. N. Sakai, Naturalnes in supersymmetric GUTS. Z. Phys. C 11, 153 (1981)

    Article  ADS  Google Scholar 

  16. W.J. Marciano, G. Senjanović, Predictions of supersymmetric grand unified theories. Phys. Rev. D 25, 3092 (1982)

    Article  ADS  Google Scholar 

  17. M.B. Einhorn, D.R.T. Jones, The weak mixing angle and unification mass in supersymmetric SU(5). Nucl. Phys. B 196, 475 (1982)

    Article  ADS  Google Scholar 

  18. L.E. Ibáñez, G.G. Ross, Low-energy predictions in supersymmetric grand unified theories. Phys. Lett. B 105, 439 (1981)

    Article  ADS  Google Scholar 

  19. T.W.B. Kibble, Some implications of a cosmological phase transition. Phys. Rep. 67, 183 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  20. M.B. Hindmarsh, T.W.B. Kibble, Cosmic strings. Rep. Prog. Phys. 58, 477 (1995). [arXiv:hep-ph/9411342]

  21. A. Vilenkin, E.P.S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  22. D. Tong, TASI lectures on solitons. arXiv:hep-th/0509216

  23. R.J. Danos, R.H. Brandenberger, G. Holder, Signature of cosmic strings wakes in the CMB polarization. Phys. Rev. D 82, 023513 (2010). [arXiv:1003.0905]

  24. N. Bevis, M. Hindmarsh, M. Kunz, J. Urrestilla, CMB power spectra from cosmic strings: predictions for the Planck satellite and beyond. Phys. Rev. D 82, 065004 (2010). [arXiv:1005.2663]

  25. Ya.B. Zel’dovich, M.Y. Khlopov, On the concentration of relic magnetic monopoles in the universe. Phys. Lett. B 79, 239 (1978)

  26. J. Preskill, Cosmological production of superheavy magnetic monopoles. Phys. Rev. Lett. 43, 1365 (1979)

    Article  ADS  Google Scholar 

  27. J. Preskill, Magnetic monopoles. Ann. Rev. Nucl. Part. Sci. 34, 461 (1984)

    Article  ADS  Google Scholar 

  28. V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Cambridge, 2005)

    Book  MATH  Google Scholar 

  29. S. Weinberg, Cosmology (Oxford University Press, Oxford, 2008)

    MATH  Google Scholar 

  30. K. Sato, Cosmological baryon-number domain structure and the first order phase transition of a vacuum. Phys. Lett. B 99, 66 (1981)

    Article  ADS  Google Scholar 

  31. D. Kazanas, Dynamics of the universe and spontaneous symmetry breaking. Astrophys. J. 241, L59 (1980)

    Article  ADS  Google Scholar 

  32. A.H. Guth, Inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347 (1981)

    Article  ADS  Google Scholar 

  33. K. Sato, First-order phase transition of a vacuum and the expansion of the universe. Mon. Not. R. Astron. Soc. 195, 467 (1981)

    Article  ADS  Google Scholar 

  34. A.R. Liddle, P. Parsons, J.D. Barrow, Formalising the slow-roll approximation in inflation. Phys. Rev. D 50, 7222 (1994). [arXiv:astro-ph/9408015]

  35. A.D. Linde, A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Phys. Lett. B 108, 389 (1982)

    Article  ADS  Google Scholar 

  36. A. Albrecht, P.J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking. Phys. Rev. Lett. 48, 1220 (1982)

    Article  ADS  Google Scholar 

  37. J.M. Bardeen, P.J. Steinhardt, M.S. Turner, Spontaneous creation of almost scale-free density perturbations in an inflationary universe. Phys. Rev. D 28, 679 (1983)

    Article  ADS  Google Scholar 

  38. A.A. Starobinsky, Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations. Phys. Lett. B 117, 175 (1982)

    Article  ADS  Google Scholar 

  39. S.W. Hawking, The development of irregularities in a single bubble inflationary universe. Phys. Lett. B 115, 295 (1982)

    Article  ADS  Google Scholar 

  40. A.D. Linde, Scalar field fluctuations in expanding universe and the new inflationary universe scenario. Phys. Lett. B 116, 335 (1982)

    Article  ADS  Google Scholar 

  41. A.H. Guth, S.-Y. Pi, Fluctuations in the new inflationary universe. Phys. Rev. Lett. 49, 1110 (1982)

    Article  ADS  Google Scholar 

  42. A.D. Linde, Chaotic inflation. Phys. Lett. B 129, 177 (1983)

    Article  ADS  Google Scholar 

  43. P.A.R. Ade et al. [Planck Collaboration], Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016). [arXiv:1502.01589]

  44. A.D. Linde, Can we have inflation with Ω > 1? JCAP 0305, 002 (2003). [arXiv:astro-ph/0303245]

  45. S. del Campo, R. Herrera, Extended closed inflationary universes. Class. Quantum Grav. 22, 2687 (2005). [arXiv:gr-qc/0505084]

  46. M. Kamionkowski, D.N. Spergel, N. Sugiyama, Small scale cosmic microwave background anisotropies as a probe of the geometry of the universe. Astrophys. J. 426, L57 (1994). [arXiv:astro-ph/9401003]

  47. J.R. Gott, Creation of open universes from de Sitter space. Nature 295, 304 (1982)

    Article  ADS  Google Scholar 

  48. D.H. Lyth, E.D. Stewart, Inflationary density perturbations with Ω < 1. Phys. Lett. B 252, 336 (1990)

  49. B. Ratra, P.J.E. Peebles, CDM cosmogony in an open universe. Astrophys. J. 432, L5 (1994)

    Article  ADS  Google Scholar 

  50. A. Kashlinsky, I.I. Tkachev, J. Frieman, Microwave background anisotropy in low Ω 0 inflationary models and the scale of homogeneity in the universe. Phys. Rev. Lett. 73, 1582 (1994). [arXiv:astro-ph/9405024]

  51. N. Sugiyama, J. Silk, The imprint of Ω on the cosmic microwave background. Phys. Rev. Lett. 73, 509 (1994). [arXiv:astro-ph/9406026]

  52. M. Kamionkowski, B. Ratra, D.N. Spergel, N. Sugiyama, CBR anisotropy in an open inflation, CDM cosmogony. Astrophys. J. 434, L1 (1994). [arXiv:astro-ph/9406069]

  53. B. Ratra, P.J.E. Peebles, Inflation in an open universe. Phys. Rev. D 52, 1837 (1995)

    Article  ADS  Google Scholar 

  54. M. Bucher, A.S. Goldhaber, N. Turok, An open universe from inflation. Phys. Rev. D 52, 3314 (1995). [arXiv:hep-ph/9411206]

  55. K. Yamamoto, M. Sasaki, T. Tanaka, Large angle CMB anisotropy in an open universe in the one bubble inflationary scenario. Astrophys. J. 455, 412 (1995). [arXiv:astro-ph/9501109]

  56. A.D. Linde, Inflation with variable Ω. Phys. Lett. B 351, 99 (1995). [arXiv:hep-th/9503097]

  57. A.D. Linde, Toy model for open inflation. Phys. Rev. D 59, 023503 (1999). [arXiv:hep-ph/9807493]

  58. A.D. Linde, M. Sasaki, T. Tanaka, CMB in open inflation. Phys. Rev. D 59, 123522 (1999). [arXiv:astro-ph/9901135]

  59. S. del Campo, R. Herrera, Extended open inflationary universes. Phys. Rev. D 67, 063507 (2003). [arXiv:gr-qc/0303024]

  60. B. Freivogel, M. Kleban, M. Rodríguez Martínez, L. Susskind, Observational consequences of a landscape. JHEP 0603, 039 (2006). [arXiv:hep-th/0505232]

  61. D. Yamauchi, A. Linde, A. Naruko, M. Sasaki, T. Tanaka, Open inflation in the landscape. Phys. Rev. D 84, 043513 (2011). [arXiv:1105.2674]

  62. M. Joyce, Electroweak baryogenesis and the expansion rate of the universe. Phys. Rev. D 55, 1875 (1997). [arXiv:hep-ph/9606223]

  63. J.H. Kung, R.H. Brandenberger, Chaotic inflation as an attractor in initial-condition space. Phys. Rev. D 42, 1008 (1990)

    Article  ADS  Google Scholar 

  64. A.D. Dolgov, A.D. Linde, Baryon asymmetry in the inflationary universe. Phys. Lett. B 116, 329 (1982)

    Article  ADS  Google Scholar 

  65. L.F. Abbott, E. Fahri, M.B. Wise, Particle production in the new inflationary cosmology. Phys. Lett. B 117, 29 (1982)

    Article  ADS  Google Scholar 

  66. A.D. Dolgov, D.P. Kirilova, Production of particles by a variable scalar field. Sov. J. Nucl. Phys. 51, 172 (1990)

    Google Scholar 

  67. J.H. Traschen, R.H. Brandenberger, Particle production during out-of-equilibrium phase transitions. Phys. Rev. D 42, 2491 (1990)

    Article  ADS  Google Scholar 

  68. L. Kofman, A.D. Linde, A.A. Starobinsky, Reheating after inflation. Phys. Rev. Lett. 73, 3195 (1994). [arXiv:hep-th/9405187]

  69. Y. Shtanov, J.H. Traschen, R.H. Brandenberger, Universe reheating after inflation. Phys. Rev. D 51, 5438 (1995). [arXiv:hep-ph/9407247]

  70. D. Boyanovsky, H.J. de Vega, R. Holman, D.S. Lee, A. Singh, Dissipation via particle production in scalar field theories. Phys. Rev. D 51, 4419 (1995). [arXiv:hep-ph/9408214]

  71. D.I. Kaiser, Post inflation reheating in an expanding universe. Phys. Rev. D 53, 1776 (1996). [arXiv:astro-ph/9507108]

  72. D. Boyanovsky, M. D’Attanasio, H.J. de Vega, R. Holman, D.S. Lee, Linear versus nonlinear relaxation: consequences for reheating and thermalization. Phys. Rev. D 52, 6805 (1995). [arXiv:hep-ph/9507414]

  73. S.Yu. Khlebnikov, I.I. Tkachev, Classical decay of inflaton. Phys. Rev. Lett. 77, 219 (1996). [arXiv:hep-ph/9603378]

  74. S.Yu. Khlebnikov, I.I. Tkachev, The universe after inflation: the wide resonance case. Phys. Lett. B 390, 80 (1997). [arXiv:hep-ph/9608458]

  75. T. Prokopec, T.G. Roos, Lattice study of classical inflaton decay. Phys. Rev. D 55, 3768 (1997). [arXiv:hep-ph/9610400]

  76. S.Yu. Khlebnikov, I.I. Tkachev, Resonant decay of Bose condensates. Phys. Rev. Lett. 79, 1607 (1997). [arXiv:hep-ph/9610477]

  77. D. Boyanovsky, D. Cormier, H.J. de Vega, R. Holman, A. Singh, M. Srednicki, Scalar field dynamics in Friedman–Robertson–Walker spacetimes. Phys. Rev. D 56, 1939 (1997). [arXiv:hep-ph/9703327]

  78. L. Kofman, A.D. Linde, A.A. Starobinsky, Towards the theory of reheating after inflation. Phys. Rev. D 56, 3258 (1997). [arXiv:hep-ph/9704452]

  79. B.A. Bassett, S. Liberati, Geometric reheating after inflation. Phys. Rev. D 58, 021302(R) (1998); Erratum-ibid. 60, 049902(E) (1999). [arXiv:hep-ph/9709417]

  80. B.A. Bassett, S. Tsujikawa, D. Wands, Inflation dynamics and reheating. Rev. Mod. Phys. 78, 537 (2006). [arXiv:astro-ph/0507632]

  81. P.B. Greene, L. Kofman, A.D. Linde, A.A. Starobinsky, Structure of resonance in preheating after inflation. Phys. Rev. D 56, 6175 (1997). [arXiv:hep-ph/9705347]

  82. B.A. Bassett, D.I. Kaiser, R. Maartens, General relativistic preheating after inflation. Phys. Lett. B 455, 84 (1999). [arXiv:hep-ph/9808404]

  83. G.N. Felder, L. Kofman, A.D. Linde, Instant preheating. Phys. Rev. D 59, 123523 (1999). [arXiv:hep-ph/9812289]

  84. M. Kawasaki, K. Kohri, T. Moroi, Big-bang nucleosynthesis and hadronic decay of long-lived massive particles. Phys. Rev. D 71, 083502 (2005). [arXiv:astro-ph/0408426]

  85. K. Kohri, T. Moroi, A. Yotsuyanagi, Big-bang nucleosynthesis with unstable gravitino and upper bound on the reheating temperature. Phys. Rev. D 73, 123511 (2006). [arXiv:hep-ph/0507245]

  86. A.R. Liddle, S.M. Leach, How long before the end of inflation were observable perturbations produced? Phys. Rev. D 68, 103503 (2003). [arXiv:astro-ph/0305263]

  87. D.H. Lyth, A.R. Liddle, The Primordial Density Perturbation (Cambridge University Press, Cambridge, 2009)

    Book  MATH  Google Scholar 

  88. http://map.gsfc.nasa.gov

  89. D.S. Salopek, J.R. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models. Phys. Rev. D 42, 3936 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  90. A.G. Muslimov, On the scalar field dynamics in a spatially flat Friedmann universe. Class. Quantum Grav. 7, 231 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  91. P.J. Steinhardt, M.S. Turner, Prescription for successful new inflation. Phys. Rev. D 29, 2162 (1984)

    Article  ADS  Google Scholar 

  92. A.R. Liddle, D.H. Lyth, COBE, gravitational waves, inflation and extended inflation. Phys. Lett. B 291, 391 (1992). [arXiv:astro-ph/9208007]

  93. E.W. Kolb, S.L. Vadas, Relating spectral indices to tensor and scalar amplitudes in inflation. Phys. Rev. D 50, 2479 (1994). [arXiv:astro-ph/9403001]

  94. D.J. Schwarz, C.A. Terrero-Escalante, A.A. García, Higher order corrections to primordial spectra from cosmological inflation. Phys. Lett. B 517, 243 (2001). [arXiv:astro-ph/0106020]

  95. W.H. Kinney, Inflation: flow, fixed points, and observables to arbitrary order in slow roll. Phys. Rev. D 66, 083508 (2002). [arXiv:astro-ph/0206032]

  96. A.R. Liddle, Inflationary flow equations. Phys. Rev. D 68, 103504 (2003). [arXiv:astro-ph/0307286]

  97. E. Ramírez, A.R. Liddle, Stochastic approaches to inflation model building. Phys. Rev. D 71, 123510 (2005). [arXiv:astro-ph/0502361]

  98. E.J. Copeland, M.R. Garousi, M. Sami, S. Tsujikawa, What is needed of a tachyon if it is to be the dark energy? Phys. Rev. D 71, 043003 (2005). [arXiv:hep-th/0411192]

  99. S. Dodelson, W.H. Kinney, E.W. Kolb, Cosmic microwave background measurements can discriminate among inflation models. Phys. Rev. D 56, 3207 (1997). [arXiv:astro-ph/9702166]

  100. L. Alabidi, D.H. Lyth, Inflation models and observation. JCAP 0605, 016 (2006). [arXiv:astro-ph/0510441]

  101. C. Wetterich, Kaluza–Klein cosmology and the inflationary universe. Nucl. Phys. B 252, 309 (1985)

    Article  ADS  Google Scholar 

  102. Q. Shafi, C. Wetterich, Inflation with higher dimensional gravity. Phys. Lett. B 152, 51 (1985)

    Article  ADS  Google Scholar 

  103. Q. Shafi, C. Wetterich, Inflation from higher dimensions. Nucl. Phys. B 289, 787 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  104. H. Nishino, E. Sezgin, Matter and gauge couplings of N = 2 supergravity in six dimensions. Phys. Lett. B 144, 187 (1984)

  105. A. Salam, E. Sezgin, Chiral compactification on Minkowski × S 2 of N = 2 Einstein–Maxwell supergravity in six dimensions. Phys. Lett. B 147, 47 (1984)

  106. S. Randjbar-Daemi, A. Salam, E. Sezgin, J.A. Strathdee, An anomaly-free model in six dimensions. Phys. Lett. B 151, 351 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  107. I.G. Koh, H. Nishino, Towards realistic D = 6, N = 2 Kaluza–Klein supergravity on coset E7∕SO(12) × Sp(1) with chiral fermions. Phys. Lett. B 153, 45 (1985)

  108. K.-i. Maeda, H. Nishino, Cosmological solutions in D = 6, N = 2 Kaluza–Klein supergravity: Friedmann universe without fine tuning. Phys. Lett. B 154, 358 (1985)

  109. K.-i. Maeda, H. Nishino, An attractor universe in six-dimensional N = 2 supergravity Kaluza–Klein theory. Phys. Lett. B 158, 381 (1985)

  110. J.J. Halliwell, Classical and quantum cosmology of the Salam–Sezgin model. Nucl. Phys. B 286, 729 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  111. P.A.R. Ade et al. [Planck Collaboration], Planck 2015. XX. Constraints on inflation. Astron. Astrophys. 594, A20 (2016). [arXiv:1502.02114]

  112. K. Freese, J.A. Frieman, A.V. Olinto, Natural inflation with pseudo Nambu–Goldstone bosons. Phys. Rev. Lett. 65, 3233 (1990)

    Article  ADS  Google Scholar 

  113. F.C. Adams, J.R. Bond, K. Freese, J.A. Frieman, A.V. Olinto, Natural inflation: particle physics models, power-law spectra for large-scale structure, and constraints from COBE. Phys. Rev. D 47, 426 (1993). [arXiv:hep-ph/9207245]

  114. J.E. Kim, H.P. Nilles, M. Peloso, Completing natural inflation. JCAP 0501, 005 (2005). [arXiv:hep-ph/0409138]

  115. M. Sasaki, E.D. Stewart, A general analytic formula for the spectral index of the density perturbations produced during inflation. Prog. Theor. Phys. 95, 71 (1996). [arXiv:astro-ph/9507001]

  116. A.A. Starobinsky, Multicomponent de Sitter (inflationary) stages and the generation of perturbations. Pis’ma Zh. Eksp. Teor. Fiz. 42, 124 (1985) [JETP Lett. 42, 152 (1985)]

  117. J. Silk, M.S. Turner, Double inflation. Phys. Rev. D 35. 419 (1987)

  118. D.S. Salopek, J.R. Bond, J.M. Bardeen, Designing density fluctuation spectra in inflation. Phys. Rev. D 40, 1753 (1989)

    Article  ADS  Google Scholar 

  119. A.R. Liddle, A. Mazumdar, F.E. Schunck, Assisted inflation. Phys. Rev. D 58, 061301 (1998). [arXiv:astro-ph/9804177]

  120. K.A. Malik, D. Wands, Dynamics of assisted inflation. Phys. Rev. D 59, 123501 (1999). [arXiv:astro-ph/9812204]

  121. A.A. Coley, R.J. van den Hoogen, Dynamics of multi-scalar-field cosmological models and assisted inflation. Phys. Rev. D 62, 023517 (2000). [arXiv:gr-qc/9911075]

  122. J.M. Aguirregabiria, A. Chamorro, L.P. Chimento, N.A. Zuccalá, Assisted inflation in Friedmann–Robertson–Walker and Bianchi spacetimes. Phys. Rev. D 62, 084029 (2000). [arXiv:gr-qc/0006108]

  123. P. Kanti, K.A. Olive, Realization of assisted inflation. Phys. Rev. D 60, 043502 (1999). [arXiv:hep-ph/9903524]

  124. Z.K. Guo, Y.S. Piao, Y.Z. Zhang, Cosmological scaling solutions and multiple exponential potentials. Phys. Lett. B 568, 1 (2003). [arXiv:hep-th/0304048]

  125. S.A Kim, A.R. Liddle, S. Tsujikawa, Dynamics of assisted quintessence. Phys. Rev. D 72, 043506 (2005). [arXiv:astro-ph/0506076]

  126. Z.K. Guo, Y.S. Piao, R.G. Cai, Y.Z. Zhang, Cosmological scaling solutions and cross-coupling exponential potential. Phys. Lett. B 576, 12 (2003). [arXiv:hep-th/0306245]

  127. A. Collinucci, M. Nielsen, T. Van Riet, Scalar cosmology with multi-exponential potentials. Class. Quantum Grav. 22, 1269 (2005). [arXiv:hep-th/0407047]

  128. J. Hartong, A. Ploegh, T. Van Riet, D.B. Westra, Dynamics of generalized assisted inflation. Class. Quantum Grav. 23, 4593 (2006). [arXiv:gr-qc/0602077]

  129. G. Calcagni, A.R. Liddle, Stability of multifield cosmological solutions. Phys. Rev. D 77, 023522 (2008). [arXiv:0711.3360]

  130. S. Tsujikawa, General analytic formulae for attractor solutions of scalar-field dark energy models and their multifield generalizations. Phys. Rev. D 73, 103504 (2006). [arXiv:hep-th/0601178]

  131. J.c. Hwang, H. Noh, Cosmological perturbations with multiple scalar fields. Phys. Lett. B 495, 277 (2000). [arXiv:astro-ph/0009268]

  132. D. Langlois, F. Vernizzi, Nonlinear perturbations of cosmological scalar fields. JCAP 0702, 017 (2007). [arXiv:astro-ph/0610064]

  133. G.I. Rigopoulos, E.P.S. Shellard, B.J.W. van Tent, Nonlinear perturbations in multiple-field inflation. Phys. Rev. D 73, 083521 (2006). [arXiv:astro-ph/0504508]

  134. M. Sasaki, T. Tanaka, Super-horizon scale dynamics of multi-scalar inflation. Prog. Theor. Phys. 99, 763 (1998). [arXiv:gr-qc/9801017]

  135. T.J. Allen, B. Grinstein, M.B. Wise, Non-gaussian density perturbations in inflationary cosmologies. Phys. Lett. B 197, 66 (1987)

    Article  ADS  Google Scholar 

  136. L. Kofman, D.Yu. Pogosyan, Nonflat perturbations in inflationary cosmology. Phys. Lett. B 214, 508 (1988)

    Article  ADS  Google Scholar 

  137. S. Mollerach, S. Matarrese, A. Ortolan, F. Lucchin, Stochastic inflation in a simple two-field model. Phys. Rev. D 44, 1670 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  138. A.D. Linde, V. Mukhanov, Non-Gaussian isocurvature perturbations from inflation. Phys. Rev. D 56, 535 (1997). [arXiv:astro-ph/9610219]

  139. D.H. Lyth, D. Wands, Generating the curvature perturbation without an inflaton. Phys. Lett. B 524, 5 (2002). [arXiv:hep-ph/0110002]

  140. D.H. Lyth, C. Ungarelli, D. Wands, The primordial density perturbation in the curvaton scenario. Phys. Rev. D 67, 023503 (2003). [arXiv:astro-ph/0208055]

  141. N. Bartolo, S. Matarrese, A. Riotto, Non-Gaussianity in the curvaton scenario. Phys. Rev. D 69, 043503 (2004). [arXiv:hep-ph/0309033]

  142. A.D. Linde, Eternal extended inflation and graceful exit from old inflation without Jordan–Brans–Dicke. Phys. Lett. B 249, 18 (1990)

    Article  ADS  Google Scholar 

  143. A.D. Linde, Axions in inflationary cosmology. Phys. Lett. B 259, 38 (1991)

    Article  ADS  Google Scholar 

  144. A.D. Linde, Hybrid inflation. Phys. Rev. D 49, 748 (1994). [arXiv:astro-ph/9307002]

  145. S. Mollerach, S. Matarrese, F. Lucchin, Blue perturbation spectra from inflation. Phys. Rev. D 50, 4835 (1994). [arXiv:astro-ph/9309054]

  146. E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, D. Wands, False vacuum inflation with Einstein gravity. Phys. Rev. D 49, 6410 (1994). [arXiv:astro-ph/9401011]

  147. S. Tsujikawa, J. Ohashi, S. Kuroyanagi, A. De Felice, Planck constraints on single-field inflation. Phys. Rev. D 88, 023529 (2013). [arXiv:1305.3044]

  148. J.A. Wheeler, W.H. Zurek (eds.), Quantum Theory and Measurement (Princeton University Press, Princeton, 1983)

    Google Scholar 

  149. H. Everett, “Relative state” formulation of quantum mechanics. Rev. Mod. Phys. 29, 454 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  150. J.B. Hartle, Quantum mechanics of individual systems. Am. J. Phys. 36, 704 (1968)

    Article  ADS  Google Scholar 

  151. B.S. DeWitt, R.N. Graham (eds.), The Many-Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1973)

    Google Scholar 

  152. W.H. Zurek, Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  153. N. Pinto-Neto, G. Santos, W. Struyve, Quantum-to-classical transition of primordial cosmological perturbations in de Broglie–Bohm quantum theory. Phys. Rev. D 85, 083506 (2012). [arXiv:1110.1339]

  154. E. Joos, H.D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, I.-O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 2003)

    Book  MATH  Google Scholar 

  155. M. Schlosshauer, Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics. Ann. Phys. (N.Y.) 321, 112 (2006). [arXiv:quant-ph/0506199]

  156. H.D. Zeh, Emergence of classical time from a universal wave function. Phys. Lett. A 116, 9 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  157. C. Kiefer, Continuous measurement of mini-superspace variables by higher multipoles. Class. Quantum Grav. 4, 1369 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  158. M. Sakagami, Evolution from pure states into mixed states in de Sitter space. Prog. Theor. Phys. 79, 442 (1988)

    Article  ADS  Google Scholar 

  159. J.J. Halliwell, Decoherence in quantum cosmology. Phys. Rev. D 39, 2912 (1989)

    Article  ADS  Google Scholar 

  160. T. Padmanabhan, Decoherence in the density matrix describing quantum three-geometries and the emergence of classical spacetime. Phys. Rev. D 39, 2924 (1989)

    Article  ADS  Google Scholar 

  161. J.P. Paz, S. Sinha, Decoherence and back reaction: the origin of the semiclassical Einstein equations. Phys. Rev. D 44, 1038 (1991)

    Article  ADS  Google Scholar 

  162. C. Kiefer, Decoherence in quantum electrodynamics and quantum gravity. Phys. Rev. D 46, 1658 (1992)

    Article  ADS  Google Scholar 

  163. C. Kiefer, Topology, decoherence, and semiclassical gravity. Phys. Rev. D 47, 5414 (1993). [arXiv:gr-qc/9306016]

  164. I.G. Moss, Quantum Theory, Black Holes and Inflation (Wiley, Chichester, 1996)

    MATH  Google Scholar 

  165. L.P. Grishchuk, Amplification of gravitational waves in an isotropic universe. Zh. Eksp. Teor. Fiz. 67, 825 (1974) [Sov. Phys. JETP 40, 409 (1975)]

  166. L.H. Ford, L. Parker, Quantized gravitational wave perturbations in Robertson–Walker universes. Phys. Rev. D 16, 1601 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  167. N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982)

    Book  MATH  Google Scholar 

  168. T.S. Bunch, P.C.W. Davies, Quantum field theory in de Sitter space: renormalization by point splitting. Proc. R. Soc. Lond. A 360, 117 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  169. R.H. Brandenberger, Quantum fluctuations as the source of classical gravitational perturbations in inflationary universe models. Nucl. Phys. B 245, 328 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  170. M.R. Brown, C.R. Dutton, Energy-momentum tensor and definition of particle states for Robertson–Walker space-times. Phys. Rev. D 18, 4422 (1978)

    Article  ADS  Google Scholar 

  171. J. Martin, R.H. Brandenberger, The trans-Planckian problem of inflationary cosmology. Phys. Rev. D 63, 123501 (2001). [arXiv:hep-th/0005209]

  172. N.A. Chernikov, E.A. Tagirov, Quantum theory of scalar fields in de Sitter space-time. Ann. Poincaré Phys. Theor. A 9, 109 (1968)

    MATH  MathSciNet  Google Scholar 

  173. E.A. Tagirov, Consequences of field quantization in de Sitter type cosmological models. Ann. Phys. (N.Y.) 76, 561 (1973)

  174. J. Géhéniau, C. Schomblond, Fonctions de Green dans l’univers de de Sitter. Acad. R. Belg. Bull. Cl. Sci. 54, 1147 (1968)

    MathSciNet  Google Scholar 

  175. C. Schomblond, P. Spindel, Uniqueness conditions for the \(\Delta ^{1}(x,y)\) propagator of the scalar field in the de Sitter universe. Ann. Poincaré Phys. Theor. A 25, 67 (1976)

  176. E. Mottola, Particle creation in de Sitter space. Phys. Rev. D 31, 754 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  177. B. Allen, Vacuum states in de Sitter space. Phys. Rev. D 32, 3136 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  178. B. Allen, A. Folacci, Massless minimally coupled scalar field in de Sitter space. Phys. Rev. D 35, 3771 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  179. R. Bousso, A. Maloney, A. Strominger, Conformal vacua and entropy in de Sitter space. Phys. Rev. D 65, 104039 (2002). [arXiv:hep-th/0112218]

  180. M. Spradlin, A. Volovich, Vacuum states and the S-matrix in dS/CFT. Phys. Rev. D 65, 104037 (2002). [arXiv:hep-th/0112223]

  181. D. Polarski, A.A. Starobinsky, Semiclassicality and decoherence of cosmological perturbations. Class. Quantum Grav. 13, 377 (1996). [arXiv:gr-qc/9504030]

  182. U.H. Danielsson, Note on inflation and trans-Planckian physics. Phys. Rev. D 66, 023511 (2002). [arXiv:hep-th/0203198]

  183. U.H. Danielsson, Inflation, holography and the choice of vacuum in de Sitter space. JHEP 0207, 040 (2002). [arXiv:hep-th/0205227]

  184. N. Kaloper, M. Kleban, A. Lawrence, S. Shenker, L. Susskind, Initial conditions for inflation. JHEP 0211, 037 (2002). [arXiv:hep-th/0209231]

  185. U.H. Danielsson, On the consistency of de Sitter vacua. JHEP 0212, 025 (2002). [arXiv:hep-th/0210058]

  186. J. Lesgourgues, D. Polarski, A.A. Starobinsky, Quantum to classical transition of cosmological perturbations for nonvacuum initial states. Nucl. Phys. B 497, 479 (1997). [arXiv:gr-qc/9611019]

  187. J. Martin, A. Riazuelo, M. Sakellariadou, Nonvacuum initial states for cosmological perturbations of quantum-mechanical origin. Phys. Rev. D 61, 083518 (2000). [arXiv:astro-ph/9904167]

  188. R.H. Brandenberger, C.T. Hill, Energy-density fluctuations in de Sitter space. Phys. Lett. B 179, 30 (1986)

    Article  ADS  Google Scholar 

  189. E.D. Stewart, D.H. Lyth, A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation. Phys. Lett. B 302, 171 (1993). [arXiv:gr-qc/9302019]

  190. E.J. Copeland, E.W. Kolb, A.R. Liddle, J.E. Lidsey, Reconstructing the inflaton potential: perturbative reconstruction to second order. Phys. Rev. D 49, 1840 (1994). [arXiv:astro-ph/9308044]

  191. D.H. Lyth, E.D. Stewart, The curvature perturbation in power law (e.g. extended) inflation. Phys. Lett. B 274, 168 (1992)

  192. C. Kiefer, D. Polarski, Why do cosmological perturbations look classical to us? Adv. Sci. Lett. 2, 164 (2009). [arXiv:0810.0087]

  193. A. Riotto, Inflation and the theory of cosmological perturbations. arXiv:hep-ph/0210162

  194. P.J. Steinhardt, Natural inflation, in The Very Early Universe, ed. by G.W. Gibbons, S.W. Hawking, S.T.C. Siklos (Cambridge University Press, Cambridge, 1983)

    Google Scholar 

  195. A. Vilenkin, Birth of inflationary universes. Phys. Rev. D 27, 2848 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  196. A.D. Linde, Eternally existing selfreproducing chaotic inflationary universe. Phys. Lett. B 175, 395 (1986)

    Article  ADS  Google Scholar 

  197. A.D. Linde, Eternal chaotic inflation. Mod. Phys. Lett. A 01, 81 (1986)

    Article  ADS  Google Scholar 

  198. A.A. Starobinsky, Stochastic de sitter (inflationary) stage in the early universe. Lect. Notes Phys. 246, 107 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  199. A.S. Goncharov, A.D. Linde, V.F. Mukhanov, The global structure of the inflationary universe. Int. J. Mod. Phys. A 2, 561 (1987)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  200. M. Aryal, A. Vilenkin, The fractal dimension of the inflationary universe. Phys. Lett. B 199, 351 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  201. K. Nakao, Y. Nambu, M. Sasaki, Stochastic dynamics of new inflation. Prog. Theor. Phys. 80, 1041 (1988)

    Article  ADS  Google Scholar 

  202. A.D. Linde, D.A. Linde, A. Mezhlumian, From the big bang theory to the theory of a stationary universe. Phys. Rev. D 49, 1783 (1994). [arXiv:gr-qc/9306035]

  203. A.D. Linde, D.A. Linde, A. Mezhlumian, Do we live in the center of the world? Phys. Lett. B 345, 203 (1995). [arXiv:hep-th/9411111]

  204. S. Winitzki, Eternal Inflation (World Scientific, Singapore, 2009)

    Book  MATH  Google Scholar 

  205. A.D. Linde, Towards a gauge invariant volume-weighted probability measure for eternal inflation. JCAP 0706, 017 (2007). [arXiv:0705.1160]

  206. A. Borde, Geodesic focusing, energy conditions and singularities. Class. Quantum Grav. 4, 343 (1987)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  207. A. Vilenkin, Did the universe have a beginning? Phys. Rev. D 46, 2355 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  208. F. Helmer, S. Winitzki, Self-reproduction in k-inflation. Phys. Rev. D 74, 063528 (2006). [arXiv:gr-qc/0608019]

  209. A. Vilenkin, Quantum fluctuations in the new inflationary Universe. Nucl. Phys. B 226, 527 (1983)

    Article  ADS  Google Scholar 

  210. A. Vilenkin, Making predictions in eternally inflating universe. Phys. Rev. D 52, 3365 (1995). [arXiv:gr-qc/9505031]

  211. A. Vilenkin, Unambiguous probabilities in an eternally inflating universe. Phys. Rev. Lett. 81, 5501 (1998). [arXiv:hep-th/9806185]

  212. V. Vanchurin, A. Vilenkin, S. Winitzki, Predictability crisis in inflationary cosmology and its resolution. Phys. Rev. D 61, 083507 (2000). [arXiv:gr-qc/9905097]

  213. J. Garriga, A. Vilenkin, Prescription for probabilities in eternal inflation. Phys. Rev. D 64, 023507 (2001). [arXiv:gr-qc/0102090]

  214. J. Garriga, D. Schwartz-Perlov, A. Vilenkin, S. Winitzki, Probabilities in the inflationary multiverse. JCAP 0601, 017 (2006). [arXiv:hep-th/0509184]

  215. R. Easther, E.A. Lim, M.R. Martin, Counting pockets with world lines in eternal inflation. JCAP 0603, 016 (2006). [arXiv:astro-ph/0511233]

  216. R. Bousso, Holographic probabilities in eternal inflation. Phys. Rev. Lett. 97, 191302 (2006). [arXiv:hep-th/0605263]

  217. R. Bousso, B. Freivogel, I-S. Yang, Eternal inflation: the inside story. Phys. Rev. D 74, 103516 (2006). [arXiv:hep-th/0606114]

  218. H. Kodama, M. Sasaki, Cosmological perturbation theory. Prog. Theor. Phys. Suppl. 78, 1 (1984)

    Article  ADS  Google Scholar 

  219. V.F. Mukhanov, H.A. Feldman, R.H. Brandenberger, Theory of cosmological perturbations. Phys. Rep. 215, 203 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  220. J.M. Bardeen, Gauge-invariant cosmological perturbations. Phys. Rev. D 22, 1882 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  221. S. Matarrese, S. Mollerach, M. Bruni, Relativistic second-order perturbations of the Einstein-de Sitter universe. Phys. Rev. D 58, 043504 (1998). [arXiv:astro-ph/9707278]

  222. V. Acquaviva, N. Bartolo, S. Matarrese, A. Riotto, Gauge-invariant second-order perturbations and non-Gaussianity from inflation. Nucl. Phys. B 667, 119 (2003). [arXiv:astro-ph/0209156]

  223. K.A. Malik, D. Wands, Evolution of second-order cosmological perturbations. Class. Quantum Grav. 21, L65 (2004). [arXiv:astro-ph/0307055]

  224. L.F. Abbott, M.B. Wise, Constraints on generalized inflationary cosmologies. Nucl. Phys. B 244, 541 (1984)

    Article  ADS  Google Scholar 

  225. V.F. Mukhanov, Gravitational instability of the universe filled with a scalar field. Pis’ma Zh. Eksp. Teor. Fiz. 41, 402 (1985) [JETP Lett. 41, 493 (1985)]

  226. M. Sasaki, Large scale quantum fluctuations in the inflationary universe. Prog. Theor. Phys. 76, 1036 (1986)

    Article  ADS  Google Scholar 

  227. V.F. Mukhanov, Quantum theory of cosmological perturbations in R 2 gravity. Phys. Lett. B 218, 17 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  228. D.H. Lyth, What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy? Phys. Rev. Lett. 78, 1861 (1997). [arXiv:hep-ph/9606387]

  229. D. Baumann, L. McAllister, A microscopic limit on gravitational waves from D-brane inflation. Phys. Rev. D 75, 123508 (2007). [arXiv:hep-th/0610285]

  230. A. Ortolan, F. Lucchin, S. Matarrese, Non-Gaussian perturbations from inflationary dynamics. Phys. Rev. D 38, 465 (1988)

    Article  ADS  Google Scholar 

  231. H.M. Hodges, G.R. Blumenthal, L.A. Kofman, J.R. Primack, Nonstandard primordial fluctuations from a polynomial inflation potential. Nucl. Phys. B 335, 197 (1990)

    Article  ADS  Google Scholar 

  232. T. Falk, R. Rangarajan, M. Srednicki, The angular dependence of the three point correlation function of the cosmic microwave background radiation as predicted by inflationary cosmologies. Astrophys. J. 403, L1 (1993). [arXiv:astro-ph/9208001]

  233. I. Yi, E.T. Vishniac, Inflationary stochastic dynamics and the statistics of large-scale structure. Astrophys. J. Suppl. Ser. 86, 333 (1993)

    Article  ADS  Google Scholar 

  234. I. Yi, E.T. Vishniac, Simple estimate of the statistics of large scale structure. Phys. Rev. D 48, 950 (1993)

    Article  ADS  Google Scholar 

  235. G.I. Rigopoulos, E.P.S. Shellard, B.J.W. van Tent, Simple route to non-Gaussianity in inflation. Phys. Rev. D 72, 083507 (2005). [arXiv:astro-ph/0410486]

  236. D. Seery, J.E. Lidsey, Primordial non-Gaussianities in single field inflation. JCAP 0506, 003 (2005). [arXiv:astro-ph/0503692]

  237. D.H. Lyth, Y. Rodríguez, The inflationary prediction for primordial non-Gaussianity. Phys. Rev. Lett. 95, 121302 (2005). [arXiv:astro-ph/0504045]

  238. X. Chen, M.x. Huang, S. Kachru, G. Shiu, Observational signatures and non-Gaussianities of general single field inflation. JCAP 0701, 002 (2007). [arXiv:hep-th/0605045]

  239. D. Seery, J.E. Lidsey, M.S. Sloth, The inflationary trispectrum. JCAP 0701, 027 (2007). [arXiv:astro-ph/0610210]

  240. X. Chen, M.x. Huang, G. Shiu, The inflationary trispectrum for models with large non-Gaussianities. Phys. Rev. D 74, 121301 (2006). [arXiv:hep-th/0610235]

  241. F. Arroja, K. Koyama, Non-Gaussianity from the trispectrum in general single field inflation. Phys. Rev. D 77, 083517 (2008). [arXiv:0802.1167]

  242. L. Wang, M. Kamionkowski, The cosmic microwave background bispectrum and inflation. Phys. Rev. D 61, 063504 (2000). [arXiv:astro-ph/9907431]

  243. A. Gangui, J. Martin, Cosmic microwave background bispectrum and slow roll inflation. Mon. Not. R. Astron. Soc. 313, 323 (2000). [arXiv:astro-ph/9908009]

  244. A. Gangui, F. Lucchin, S. Matarrese, S. Mollerach, The three-point correlation function of the cosmic microwave background in inflationary models. Astrophys. J. 430, 447 (1994). [arXiv:astro-ph/9312033]

  245. J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models. JHEP 0305, 013 (2003). [arXiv:astro-ph/0210603]

  246. D. Babich, P. Creminelli, M. Zaldarriaga, The shape of non-Gaussianities. JCAP 0408, 009 (2004). [arXiv:astro-ph/0405356]

  247. P. Creminelli, M. Zaldarriaga, Single field consistency relation for the 3-point function. JCAP 0410, 006 (2004). [arXiv:astro-ph/0407059]

  248. L. Senatore, K.M. Smith, M. Zaldarriaga, Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data. JCAP 1001, 028 (2010). [arXiv:0905.3746]

  249. P. Creminelli, On non-Gaussianities in single-field inflation. JCAP 0310, 003 (2003). [arXiv:astro-ph/0306122]

  250. S. Gupta, A. Berera, A.F. Heavens, S. Matarrese, Non-Gaussian signatures in the cosmic background radiation from warm inflation. Phys. Rev. D 66, 043510 (2002). [arXiv:astro-ph/0205152]

  251. S. Gupta, Dynamics and non-Gaussianity in the weak-dissipative warm inflation scenario. Phys. Rev. D 73, 083514 (2006). [arXiv:astro-ph/0509676]

  252. N. Arkani-Hamed, P. Creminelli, S. Mukohyama, M. Zaldarriaga, Ghost inflation. JCAP 0404, 001 (2004). [arXiv:hep-th/0312100]

  253. K. Izumi, S. Mukohyama, Trispectrum from ghost inflation. JCAP 1006, 016 (2010). [arXiv:1004.1776]

  254. A. Gangui, J. Martin, M. Sakellariadou, Single field inflation and non-Gaussianity. Phys. Rev. D 66, 083502 (2002). [arXiv:astro-ph/0205202]

  255. S.-J. Rey, Dynamics of inflationary phase transition. Nucl. Phys. B 284, 706 (1987)

    Article  ADS  Google Scholar 

  256. A. Hosoya, M. Morikawa, K. Nakayama, Stochastic dynamics of scalar field in the inflationary universe. Int. J. Mod. Phys. A 4, 2613 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  257. D.S. Salopek, J.R. Bond, Stochastic inflation and nonlinear gravity. Phys. Rev. D 43, 1005 (1991)

    Article  ADS  Google Scholar 

  258. I. Yi, E.T. Vishniac, Stochastic analysis of the initial condition constraints on chaotic inflation. Phys. Rev. D 47, 5280 (1993)

    Article  ADS  Google Scholar 

  259. A.A. Starobinsky, J. Yokoyama, Equilibrium state of a self-interacting scalar field in the de Sitter background. Phys. Rev. D 50, 6357 (1994). [arXiv:astro-ph/9407016]

  260. J. Martin, M. Musso, Solving stochastic inflation for arbitrary potentials. Phys. Rev. D 73, 043516 (2006). [arXiv:hep-th/0511214]

  261. J. Martin, M. Musso, Reliability of the Langevin pertubative solution in stochastic inflation. Phys. Rev. D 73, 043517 (2006). [arXiv:hep-th/0511292]

  262. F. Kühnel, D.J. Schwarz, Large-scale suppression from stochastic inflation. Phys. Rev. Lett. 105, 211302 (2010). [arXiv:1003.3014]

  263. H. Haken, Synergetics (Springer, Berlin, 1978)

    Book  MATH  Google Scholar 

  264. H. Risken, The Fokker–Planck Equation (Springer, Berlin, 1984)

    Book  MATH  Google Scholar 

  265. S. Matarrese, M.A. Musso, A. Riotto, Influence of super-horizon scales on cosmological observables generated during inflation. JCAP 0405, 008 (2004). [arXiv:hep-th/0311059]

  266. G.I. Rigopoulos, E.P.S. Shellard, The separate universe approach and the evolution of nonlinear superhorizon cosmological perturbations. Phys. Rev. D 68, 123518 (2003). [arXiv:astro-ph/0306620]

  267. G.I. Rigopoulos, E.P.S. Shellard, Non-linear inflationary perturbations. JCAP 0510, 006 (2005). [arXiv:astro-ph/0405185]

  268. D.H. Lyth, K.A. Malik, M. Sasaki, A general proof of the conservation of the curvature perturbation. JCAP 0505, 004 (2005). [arXiv:astro-ph/0411220]

  269. D. Wands, K.A. Malik, D.H. Lyth, A.R. Liddle, A new approach to the evolution of cosmological perturbations on large scales. Phys. Rev. D 62, 043527 (2000). [arXiv:astro-ph/0003278]

  270. D.H. Lyth, Y. Rodríguez, Non-Gaussianity from the second-order cosmological perturbation. Phys. Rev. D 71, 123508 (2005). [arXiv:astro-ph/0502578]

  271. P.J.E. Peebles, An isocurvature cold dark matter cosmogony. I. A worked example of evolution through inflation. Astrophys. J. 510, 523 (1999). [arXiv:astro-ph/9805194]

  272. P.J.E. Peebles, An isocurvature cold dark matter cosmogony. II. Observational tests. Astrophys. J. 510, 531 (1999). [arXiv:astro-ph/9805212]

  273. F. Bernardeau, J.-P. Uzan, Non-Gaussianity in multi-field inflation. Phys. Rev. D 66, 103506 (2002). [arXiv:hep-ph/0207295]

  274. F. Bernardeau, J.-P. Uzan, Inflationary models inducing non-Gaussian metric fluctuations. Phys. Rev. D 67, 121301 (2003). [arXiv:astro-ph/0209330]

  275. M. Zaldarriaga, Non-Gaussianities in models with a varying inflaton decay rate. Phys. Rev. D 69, 043508 (2004). [arXiv:astro-ph/0306006]

  276. K. Enqvist, A. Väihkönen, Non-Gaussian perturbations in hybrid inflation. JCAP 0409, 006 (2004). [arXiv:hep-ph/0405103]

  277. D.H. Lyth, Non-Gaussianity and cosmic uncertainty in curvaton-type models. JCAP 0606, 015 (2006). [arXiv:astro-ph/0602285]

  278. K.A. Malik, D.H. Lyth, A numerical study of non-Gaussianity in the curvaton scenario. JCAP 0609, 008 (2006). [arXiv:astro-ph/0604387]

  279. M. Sasaki, J. Valiviita, D. Wands, Non-Gaussianity of the primordial perturbation in the curvaton model. Phys. Rev. D 74, 103003 (2006). [arXiv:astro-ph/0607627]

  280. K. Enqvist, S. Nurmi, Non-Gaussianity in curvaton models with nearly quadratic potential. JCAP 0510, 013 (2005). [arXiv:astro-ph/0508573]

  281. D. Seery, J.E. Lidsey, Primordial non-Gaussianities from multiple-field inflation. JCAP 0509, 011 (2005). [arXiv:astro-ph/0506056]

  282. G.I. Rigopoulos, E.P.S. Shellard, B.J.W. van Tent, Large non-Gaussianity in multiple-field inflation. Phys. Rev. D 73, 083522 (2006). [arXiv:astro-ph/0506704]

  283. D.H. Lyth, I. Zaballa, A bound concerning primordial non-Gaussianity. JCAP 0510, 005 (2005). [arXiv:astro-ph/0507608]

  284. G.I. Rigopoulos, E.P.S. Shellard, B.J.W. van Tent, Quantitative bispectra from multifield inflation. Phys. Rev. D 76, 083512 (2007). [arXiv:astro-ph/0511041]

  285. I. Zaballa, Y. Rodríguez, D.H. Lyth, Higher order contributions to the primordial non-Gaussianity. JCAP 0606, 013 (2006). [arXiv:astro-ph/0603534]

  286. F. Vernizzi, D. Wands, Non-Gaussianities in two-field inflation. JCAP 0605, 019 (2006). [arXiv:astro-ph/0603799]

  287. L. Alabidi, Non-Gaussianity for a two component hybrid model of inflation. JCAP 0610, 015 (2006). [arXiv:astro-ph/0604611]

  288. T. Battefeld, R. Easther, Non-Gaussianities in multi-field inflation. JCAP 0703, 020 (2007). [arXiv:astro-ph/0610296]

  289. D. Seery, J.E. Lidsey, Non-Gaussianity from the inflationary trispectrum. JCAP 0701, 008 (2007). [arXiv:astro-ph/0611034]

  290. C.T. Byrnes, M. Sasaki, D. Wands, The primordial trispectrum from inflation. Phys. Rev. D 74, 123519 (2006). [arXiv:astro-ph/0611075]

  291. W.H. Kinney, Constraining inflation with cosmic microwave background polarization. Phys. Rev. D 58, 123506 (1998). [arXiv:astro-ph/9806259]

  292. http://cosmologist.info/cosmomc.

  293. A. Aguirre, M. Tegmark, Multiple universes, cosmic coincidences, and other dark matters. JCAP 0501, 003 (2005). [arXiv:hep-th/0409072]

  294. D.A. Easson, B.A. Powell, Identifying the inflaton with primordial gravitational waves. Phys. Rev. Lett. 106, 191302 (2011). [arXiv:1009.3741]

  295. M. Bastero-Gil, J. Macias-Pérez, D. Santos, Nonlinear metric perturbation enhancement of primordial gravitational waves. Phys. Rev. Lett. 105, 081301 (2010). [arXiv:1005.4054]

  296. U. Seljak, U.L. Pen, N. Turok, Polarization of the microwave background in defect models. Phys. Rev. Lett. 79, 1615 (1997). [arXiv:astro-ph/9704231]

  297. N. Barnaby, R. Namba, M. Peloso, Phenomenology of a pseudo-scalar inflaton: naturally large non-Gaussianity. JCAP 1104, 009 (2011). [arXiv:1102.4333]

  298. L. Sorbo, Parity violation in the cosmic microwave background from a pseudoscalar inflaton. JCAP 1106, 003 (2011). [arXiv:1101.1525]

  299. N. Barnaby, E. Pajer, M. Peloso, Gauge field production in axion inflation: consequences for monodromy, non-Gaussianity in the CMB, and gravitational waves at interferometers. Phys. Rev. D 85, 023525 (2012). [arXiv:1110.3327]

  300. N. Bartolo, S. Matarrese, M. Peloso, M. Shiraishi, Parity-violating and anisotropic correlations in pseudoscalar inflation. JCAP 1501, 027 (2015). [arXiv:1411.2521]

  301. A. Lue, L. Wang, M. Kamionkowski, Cosmological signature of new parity-violating interactions. Phys. Rev. Lett. 83, 1506 (1999). [arXiv:astro-ph/9812088]

  302. R. Jackiw, S.-Y. Pi, Chern–Simons modification of general relativity. Phys. Rev. D 68, 104012 (2003). [arXiv:gr-qc/0308071]

  303. M. Pospelov, A. Ritz, C. Skordis, Pseudoscalar perturbations and polarization of the cosmic microwave background. Phys. Rev. Lett. 103, 051302 (2009). [arXiv:0808.0673]

  304. B. Feng, H. Li, M. Li, X. Zhang, Gravitational leptogenesis and its signatures in CMB. Phys. Lett. B 620, 27 (2005). [arXiv:hep-ph/0406269]

  305. S. Mercuri, Fermions in Ashtekar–Barbero connections formalism for arbitrary values of the Immirzi parameter. Phys. Rev. D 73, 084016 (2006). [arXiv:gr-qc/0601013]

  306. C.R. Contaldi, J. Magueijo, L. Smolin, Anomalous CMB polarization and gravitational chirality. Phys. Rev. Lett. 101, 141101 (2008). [arXiv:0806.3082]

  307. S. Mercuri, Modifications in the spectrum of primordial gravitational waves induced by instantonic fluctuations. Phys. Rev. D 84, 044035 (2011). [arXiv:1007.3732]

  308. L. Bethke, J. Magueijo, Inflationary tensor fluctuations, as viewed by Ashtekar variables, their imaginary friends. Phys. Rev. D 84, 024014 (2011). [arXiv:1104.1800]

  309. L. Bethke, J. Magueijo, Chirality of tensor perturbations for complex values of the Immirzi parameter. Class. Quantum Grav. 29, 052001 (2012). [arXiv:1108.0816]

  310. A. Gruzinov, Consistency relation for single scalar inflation. Phys. Rev. D 71, 027301 (2005). [arXiv:astro-ph/0406129]

  311. N. Bartolo, S. Matarrese, A. Riotto, Enhancement of non-Gaussianity after inflation. JHEP 0404, 006 (2004). [arXiv:astro-ph/0308088]

  312. N. Bartolo, S. Matarrese, A. Riotto, Evolution of second-order cosmological perturbations and non-Gaussianity. JCAP 0401, 003 (2004). [arXiv:astro-ph/0309692]

  313. N. Bartolo, S. Matarrese, A. Riotto, Gauge-invariant temperature anisotropies and primordial non-Gaussianity. Phys. Rev. Lett. 93, 231301 (2004). [arXiv:astro-ph/0407505]

  314. K. Enqvist, A. Jokinen, A. Mazumdar, T. Multamäki, A. Väihkönen, Non-Gaussianity from preheating. Phys. Rev. Lett. 94, 161301 (2005). [arXiv:astro-ph/0411394]

  315. N. Barnaby, J.M. Cline, Non-Gaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation. Phys. Rev. D 73, 106012 (2006). [arXiv:astro-ph/0601481]

  316. N. Bartolo, E. Komatsu, S. Matarrese, A. Riotto, Non-Gaussianity from inflation: theory and observations. Phys. Rep. 402, 103 (2004). [arXiv:astro-ph/0406398]

  317. S.W. Hawking, I.G. Moss, Supercooled phase transitions in the very early universe. Phys. Lett. B 110, 35 (1982)

    Article  ADS  Google Scholar 

  318. G.W. Gibbons, S.W. Hawking, Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 15, 2738 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  319. A.A. Starobinsky, Isotropization of arbitrary cosmological expansion given an effective cosmological constant. Pis’ma Zh. Eksp. Teor. Fiz. 37, 55 (1983) [JETP Lett. 37, 66 (1983)]

  320. R.M. Wald, Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant. Phys. Rev. D 28, 2118 (1983)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  321. L.G. Jensen, J.A. Stein-Schabes, Is inflation natural? Phys. Rev. D 35, 1146 (1987)

    Article  ADS  Google Scholar 

  322. M. Bruni, S. Matarrese, O. Pantano, A local view of the observable universe. Phys. Rev. Lett. 74, 1916 (1995). [arXiv:astro-ph/9407054]

  323. R.H. Brandenberger, J. Martin, Trans-Planckian issues for inflationary cosmology. Class. Quantum Grav. 30, 113001 (2013). [arXiv:1211.6753]

  324. R.H. Brandenberger, J. Martin, The robustness of inflation to changes in super-Planck-scale physics. Mod. Phys. Lett. A 16, 999 (2001). [arXiv:astro-ph/0005432]

  325. A.A. Starobinsky, Robustness of the inflationary perturbation spectrum to trans-Planckian physics. Pis’ma Zh. Eksp. Teor. Fiz. 73, 415 (2001) [JETP Lett. 73, 371 (2001)]. [arXiv:astro-ph/0104043]

  326. J. Martin, R.H. Brandenberger, The Corley–Jacobson dispersion relation and trans-Planckian inflation. Phys. Rev. D 65, 103514 (2002). [arXiv:hep-th/0201189]

  327. R.H. Brandenberger, J. Martin, On signatures of short distance physics in the cosmic microwave background. Int. J. Mod. Phys. A 17, 3663 (2002). [arXiv:hep-th/0202142]

  328. R. Easther, B.R. Greene, W.H. Kinney, G. Shiu, Generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation. Phys. Rev. D 66, 023518 (2002). [arXiv:hep-th/0204129]

  329. G.L. Alberghi, R. Casadio, A. Tronconi, Trans-Planckian footprints in inflationary cosmology. Phys. Lett. B 579, 1 (2004). [arXiv:gr-qc/0303035]

  330. J. Martin, R.H. Brandenberger, Dependence of the spectra of fluctuations in inflationary cosmology on trans-Planckian physics. Phys. Rev. D 68, 063513 (2003). [arXiv:hep-th/0305161]

  331. S. Cremonini, Effects of quantum deformations on the spectrum of cosmological perturbations. Phys. Rev. D 68, 063514 (2003). [arXiv:hep-th/0305244]

  332. S. Koh, S.P. Kim, D.J. Song, Gravitational wave spectrum in inflation with nonclassical states. JHEP 0412, 060 (2004). [arXiv:gr-qc/0402065]

  333. S. Shankaranarayanan, L. Sriramkumar, Trans-Planckian corrections to the primordial spectrum in the infrared and the ultraviolet. Phys. Rev. D 70, 123520 (2004). [arXiv:hep-th/0403236]

  334. L. Sriramkumar, T. Padmanabhan, Initial state of matter fields and trans-Planckian physics: can CMB observations disentangle the two? Phys. Rev. D 71, 103512 (2005). [arXiv:gr-qc/0408034]

  335. R.H. Brandenberger, J. Martin, Back-reaction and the trans-Planckian problem of inflation revisited. Phys. Rev. D 71, 023504 (2005). [arXiv:hep-th/0410223]

  336. R. Easther, W.H. Kinney, H. Peiris, Observing trans-Planckian signatures in the cosmic microwave background. JCAP 0505, 009 (2005). [arXiv:astro-ph/0412613]

  337. R. Brandenberger, X.m. Zhang, The trans-Planckian problem for inflationary cosmology revisited. arXiv:0903.2065

  338. G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking. NATO Adv. Study Inst. Ser. B Phys. 59, 135 (1980)

    Google Scholar 

  339. R. Barbieri, Looking beyond the standard model: the supersymmetric option. Riv. Nuovo Cim. 11N4, 1 (1988)

  340. J. Polchinski, Effective field theory and the Fermi surface, in Recent Directions in Particle Theory—From Superstrings and Black Holes to the Standard Model, ed. by J. Harvey, J. Polchinski (World Scientific, Singapore, 1993). [arXiv:hep-th/9210046]

    Google Scholar 

  341. C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan, L. Senatore, The effective field theory of inflation. JHEP 0803, 014 (2008). [arXiv:0709.0293]

  342. D. Seery, Infrared effects in inflationary correlation functions. Class. Quantum Grav. 27, 124005 (2010) [arXiv:1005.1649]

  343. C.T. Byrnes, M. Gerstenlauer, A. Hebecker, S. Nurmi, G. Tasinato, Inflationary infrared divergences: geometry of the reheating surface versus δ N formalism. JCAP 1008, 006 (2010). [arXiv:1005.3307]

  344. C.P. Burgess, R. Holman, L. Leblond, S. Shandera, Breakdown of semiclassical methods in de Sitter space. JCAP 1010, 017 (2010). [arXiv:1005.3551]

  345. Y. Urakawa, T. Tanaka, Infrared divergence divergence does not affect the gauge-invariant curvature perturbation. Phys. Rev. D 82, 121301 (2010). [arXiv:1007.0468]

  346. Y. Urakawa, T. Tanaka, Natural selection of inflationary vacuum required by infra-red regularity and gauge-invariance. Prog. Theor. Phys. 125, 1067 (2011). [arXiv:1009.2947]

  347. M. Gerstenlauer, A. Hebecker, G. Tasinato, Inflationary correlation functions without infrared divergences. JCAP 1106, 021 (2011). [arXiv:1102.0560]

  348. W. Xue, X. Gao, R. Brandenberger, IR divergences in inflation and entropy perturbations. JCAP 1206, 035 (2012). [arXiv:1201.0768]

  349. Y. Hosotani, Exact solution to the Einstein–Yang–Mills equation. Phys. Lett. B 147, 44 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  350. D.V. Galt’sov, M.S. Volkov, Yang–Mills cosmology. Cold matter for a hot universe. Phys. Lett. B 256, 17 (1991)

    Google Scholar 

  351. L.H. Ford, Inflation driven by a vector field. Phys. Rev. D 40, 967 (1989)

    Article  ADS  Google Scholar 

  352. A.B. Burd, J.E. Lidsey, Analysis of inflationary models driven by vector fields. Nucl. Phys. B 351, 679 (1991)

    Article  ADS  Google Scholar 

  353. M.C. Bento, O. Bertolami, P. Vargas Moniz, J.M. Mourão, P.M. Sá, On the cosmology of massive vector fields with SO(3) global symmetry. Class. Quantum Grav. 10, 285 (1993). [arXiv:gr-qc/9302034]

  354. A. Golovnev, V. Mukhanov, V. Vanchurin, Vector inflation. JCAP 0806, 009 (2008). [arXiv:0802.2068]

  355. K. Bamba, S. Nojiri, S.D. Odintsov, Inflationary cosmology and the late-time accelerated expansion of the universe in nonminimal Yang–Mills-F(R) gravity and nonminimal vector-F(R) gravity. Phys. Rev. D 77, 123532 (2008). [arXiv:0803.3384]

  356. K. Dimopoulos, M. Karčiauskas, D.H. Lyth, Y. Rodríguez, Statistical anisotropy of the curvature perturbation from vector field perturbations. JCAP 0905, 013 (2009). [arXiv:0809.1055]

  357. B. Himmetoglu, C.R. Contaldi, M. Peloso, Instability of anisotropic cosmological solutions supported by vector fields. Phys. Rev. Lett. 102, 111301 (2009). [arXiv:0809.2779]

  358. A. Golovnev, V. Mukhanov, V. Vanchurin, Gravitational waves in vector inflation. JCAP 0811, 018 (2008). [arXiv:0810.4304]

  359. E. Dimastrogiovanni, N. Bartolo, S. Matarrese, A. Riotto, Non-Gaussianity and statistical anisotropy from vector field populated inflationary models. Adv. Astron. 2010, 752670 (2010). [arXiv:1001.4049]

  360. K. Dimopoulos, Can a vector field be responsible for the curvature perturbation in the universe? Phys. Rev. D 74, 083502 (2006). [arXiv:hep-ph/0607229]

  361. K. Dimopoulos, Supergravity inspired vector curvaton. Phys. Rev. D 76, 063506 (2007). [arXiv:0705.3334]

  362. K. Dimopoulos, M. Karčiauskas, Non-minimally coupled vector curvaton. JHEP 0807, 119 (2008). [arXiv:0803.3041]

  363. S. Yokoyama, J. Soda, Primordial statistical anisotropy generated at the end of inflation. JCAP 0808, 005 (2008). [arXiv:0805.4265]

  364. S. Kanno, M. Kimura, J. Soda, S. Yokoyama, Anisotropic inflation from vector impurity. JCAP 0808, 034 (2008). [arXiv:0806.2422]

  365. M. Karčiauskas, K. Dimopoulos, D.H. Lyth, Anisotropic non-Gaussianity from vector field perturbations. Phys. Rev. D 80, 023509 (2009). [arXiv:0812.0264]

  366. M.-a. Watanabe, S. Kanno, J. Soda, Inflationary universe with anisotropic hair. Phys. Rev. Lett. 102, 191302 (2009). [arXiv:0902.2833]

  367. M. Novello, S.E. Perez Bergliaffa, J. Salim, Nonlinear electrodynamics and the acceleration of the universe. Phys. Rev. D 69, 127301 (2004). [arXiv:astro-ph/0312093]

  368. V.V. Kiselev, Vector field as a quintessence partner. Class. Quantum Grav. 21, 3323 (2004). [arXiv:gr-qc/0402095]

  369. C. Armendáriz-Picón, Could dark energy be vector-like? JCAP 0407, 007 (2004). [arXiv:astro-ph/0405267]

  370. H. Wei, R.-G. Cai, Interacting vector-like dark energy, the first and second cosmological coincidence problems. Phys. Rev. D 73, 083002 (2006). [arXiv:astro-ph/0603052]

  371. C.G. Boehmer, T. Harko, Dark energy as a massive vector field. Eur. Phys. J. C 50, 423 (2007). [arXiv:gr-qc/0701029]

  372. J. Beltrán Jiménez, A.L. Maroto, Cosmic vector for dark energy. Phys. Rev. D 78, 063005 (2008). [arXiv:0801.1486]

  373. T. Koivisto, D.F. Mota, Vector field models of inflation and dark energy. JCAP 0808, 021 (2008). [arXiv:0805.4229]

  374. C. Germani, A. Kehagias, P-nflation: generating cosmic inflation with p-forms. JCAP 0903, 028 (2009). [arXiv:0902.3667]

  375. T. Kobayashi, S. Yokoyama, Gravitational waves from p-form inflation. JCAP 0905, 004 (2009). [arXiv:0903.2769]

  376. T.S. Koivisto, D.F. Mota, C. Pitrou, Inflation from N-forms and its stability. JHEP 0909, 092 (2009). [arXiv:0903.4158]

  377. T.S. Koivisto, N.J. Nunes, Three-form cosmology. Phys. Lett. B 685, 105 (2010). [arXiv:0907.3883]

  378. C. Germani, A. Kehagias, Scalar perturbations in p-nflation: the 3-form case. JCAP 0911, 005 (2009). [arXiv:0908.0001]

  379. T.S. Koivisto, N.J. Nunes, Inflation and dark energy from three-forms. Phys. Rev. D 80, 103509 (2009). [arXiv:0908.0920]

  380. T.S. Koivisto, F.R. Urban, Three-magnetic fields. Phys. Rev. D 85, 083508 (2012) [arXiv:1112.1356]

  381. T. Banks, Relaxation of the cosmological constant. Phys. Rev. Lett. 52, 1461 (1984)

    Article  ADS  Google Scholar 

  382. C. Armendáriz-Picón, P.B. Greene, Spinors, inflation, and nonsingular cyclic cosmologies. Gen. Relat. Grav. 35, 1637 (2003). [arXiv:hep-th/0301129]

  383. B. Saha, T. Boyadjiev, Bianchi type I cosmology with scalar and spinor fields. Phys. Rev. D 69, 124010 (2004). [arXiv:gr-qc/0311045]

  384. M.O. Ribas, F.P. Devecchi, G.M. Kremer, Fermions as sources of accelerated regimes in cosmology. Phys. Rev. D 72, 123502 (2005). [arXiv:gr-qc/0511099]

  385. B. Saha, Spinor field and accelerated regimes in cosmology. Grav. Cosmol. 12, 215 (2006). [arXiv:gr-qc/0512050]

    ADS  MATH  Google Scholar 

  386. B. Saha, Nonlinear spinor field in Bianchi type-I cosmology: inflation, isotropization, and late time acceleration. Phys. Rev. D 74, 124030 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  387. C.G. Böhmer, D.F. Mota, CMB anisotropies and inflation from non-standard spinors. Phys. Lett. B 663, 168 (2008). [arXiv:0710.2003]

  388. M.O. Ribas, F.P. Devecchi, G.M. Kremer, Cosmological model with non-minimally coupled fermionic field. Europhys. Lett. 81, 19001 (2008). [arXiv:0710.5155]

  389. C.G. Böhmer, Dark spinor inflation: theory primer and dynamics. Phys. Rev. D 77, 123535 (2008). [arXiv:0804.0616]

  390. Y.-F. Cai, J. Wang, Dark energy model with spinor matter and its quintom scenario. Class. Quantum Grav. 25, 165014 (2008). [arXiv:0806.3890]

  391. D. Gredat, S. Shankaranarayanan, Modified scalar and tensor spectra in spinor driven inflation. JCAP 1001, 008 (2010). [arXiv:0807.3336]

  392. D.G. Caldi, A. Chodos, Cosmological neutrino condensates. arXiv:hep-ph/9903416

  393. T. Inagaki, X. Meng, T. Murata, Dark energy problem in a four fermion interaction model. arXiv:hep-ph/0306010

  394. F. Giacosa, R. Hofmann, M. Neubert, A model for the very early universe. JHEP 0802, 077 (2008). [arXiv:0801.0197]

  395. S. Alexander, T. Biswas, The cosmological BCS mechanism and the big bang singularity. Phys. Rev. D 80, 023501 (2009). [arXiv:0807.4468]

  396. S. Alexander, T. Biswas, G. Calcagni, Cosmological Bardeen–Cooper–Schrieffer condensate as dark energy. Phys. Rev. D 81, 043511 (2010); Erratum-ibid. D 81, 069902(E) (2010). [arXiv:0906.5161]

  397. N.J. Popławski, Cosmological constant from quarks and torsion. Ann. Phys. (Berlin) 523, 291 (2011). [arXiv:1005.0893]

  398. J.M. Weller, Fermion condensate from torsion in the reheating era after inflation. Phys. Rev. D 88, 083511 (2013). [arXiv:1307.2423]

  399. D.H. Lyth, A. Riotto, Particle physics models of inflation and the cosmological density perturbation. Phys. Rep. 314, 1 (1999). [arXiv:hep-ph/9807278]

  400. G. Aad et al. [ATLAS Collaboration], Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716, 1 (2012). [arXiv:1207.7214]

  401. S. Chatrchyan et al. [CMS Collaboration], Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716, 30 (2012). [arXiv:1207.7235]

  402. D. Carmi, A. Falkowski, E. Kuflik, T. Volansky, J. Zupan, Higgs after the discovery: a status report. JHEP 1210, 196 (2012). [arXiv:1207.1718]

  403. K.A. Olive et al. [Particle Data Group], Review of particle physics. Chin. Phys. C 38, 090001 (2014)

  404. J.J. van der Bij, Can gravity make the Higgs particle decouple? Acta Phys. Polon. B 25, 827 (1994)

    Google Scholar 

  405. J.J. van der Bij, Can gravity play a role at the electroweak scale? Int. J. Phys. 1, 63 (1995). [arXiv:hep-ph/9507389]

  406. J.L. Cervantes-Cota, H. Dehnen, Induced gravity inflation in the standard model of particle physics. Nucl. Phys. B 442, 391 (1995). [arXiv:astro-ph/9505069]

  407. F.L. Bezrukov, M. Shaposhnikov, The Standard Model Higgs boson as the inflaton. Phys. Lett. B 659, 703 (2008). [arXiv:0710.3755]

  408. A.O. Barvinsky, A.Yu. Kamenshchik, A.A. Starobinsky, Inflation scenario via the Standard Model Higgs boson and LHC. JCAP 0811, 021 (2008). [arXiv:0809.2104]

  409. F. Bezrukov, D. Gorbunov, M. Shaposhnikov, On initial conditions for the hot big bang. JCAP 0906, 029 (2009). [arXiv:0812.3622]

  410. J. García-Bellido, D.G. Figueroa, J. Rubio, Preheating in the standard model with the Higgs inflaton coupled to gravity. Phys. Rev. D 79, 063531 (2009). [arXiv:0812.4624]

  411. A. De Simone, M.P. Hertzberg, F. Wilczek, Running inflation in the Standard Model. Phys. Lett. B 678, 1 (2009). [arXiv:0812.4946]

  412. F.L. Bezrukov, A. Magnin, M. Shaposhnikov, Standard Model Higgs boson mass from inflation. Phys. Lett. B 675, 88 (2009). [arXiv:0812.4950]

  413. C.P. Burgess, H.M. Lee, M. Trott, Power-counting and the validity of the classical approximation during inflation. JHEP 0909, 103 (2009). [arXiv:0902.4465]

  414. J.L.F. Barbón, J.R. Espinosa, Naturalness of Higgs inflation. Phys. Rev. D 79, 081302 (2009). [arXiv:0903.0355]

  415. F. Bezrukov, M. Shaposhnikov, Standard model Higgs boson mass from inflation: two loop analysis. JHEP 0907, 089 (2009). [arXiv:0904.1537]

  416. A.O. Barvinsky, A.Yu. Kamenshchik, C. Kiefer, A.A. Starobinsky, C.F. Steinwachs, Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field. JCAP 0912, 003 (2009). [arXiv:0904.1698]

  417. T.E. Clark, B. Liu, S.T. Love, T. ter Veldhuis, Standard model Higgs boson-inflaton and dark matter. Phys. Rev. D 80, 075019 (2009). [arXiv:0906.5595]

  418. A.O. Barvinsky, A.Yu. Kamenshchik, C. Kiefer, A.A. Starobinsky, C.F. Steinwachs, Higgs boson, renormalization group, and naturalness in cosmology. Eur. Phys. J. C 72, 2219 (2012). [arXiv:0910.1041]

  419. A.O. Barvinsky, A.Yu. Kamenshchik, C. Kiefer, C.F. Steinwachs, Tunneling cosmological state revisited: origin of inflation with a nonminimally coupled standard model Higgs inflaton. Phys. Rev. D 81, 043530 (2010). [arXiv:0911.1408]

  420. R.N. Lerner, J. McDonald, Higgs inflation and naturalness. JCAP 1004, 015 (2010). [arXiv:0912.5463]

  421. M. Atkins, X. Calmet, On the unitarity of linearized general relativity coupled to matter. Phys. Lett. B 695, 298 (2011). [arXiv:1002.0003]

  422. C.P. Burgess, H.M. Lee, M. Trott, Comment on Higgs inflation and naturalness. JHEP 1007, 007 (2010). [arXiv:1002.2730]

  423. M.P. Hertzberg, On inflation with non-minimal coupling. JHEP 1011, 023 (2010). [arXiv:1002.2995]

  424. D.I. Kaiser, Conformal transformations with multiple scalar fields. Phys. Rev. D 81, 084044 (2010). [arXiv:1003.1159]

  425. F. Bezrukov, A. Magnin, M. Shaposhnikov, S. Sibiryakov, Higgs inflation: consistency and generalisations. JHEP 1101, 016 (2011). [arXiv:1008.5157]

  426. L.A. Popa, A. Caramete, Cosmological constraints on Higgs boson mass. Astrophys. J. 723, 803 (2010). [arXiv:1009.1293]

  427. M. Atkins, X. Calmet, Remarks on Higgs inflation. Phys. Lett. B 697, 37 (2011). [arXiv:1011.4179]

  428. F. Bauer, D.A. Demir, Higgs–Palatini inflation and unitarity. Phys. Lett. B 698, 425 (2011). [arXiv:1012.2900]

  429. R.N. Lerner, J. McDonald, Distinguishing Higgs inflation and its variants. Phys. Rev. D 83, 123522 (2011). [arXiv:1104.2468]

  430. F. Bezrukov, D. Gorbunov, M. Shaposhnikov, Late and early time phenomenology of Higgs-dependent cutoff. JCAP 1110, 001 (2011). [arXiv:1106.5019]

  431. L.A. Popa, Observational consequences of the standard model Higgs inflation variants. JCAP 1110, 025 (2011). [arXiv:1107.3436]

  432. K. Nakayama, F. Takahashi, Higgs mass and inflation. Phys. Lett. B 707, 142 (2012). [arXiv:1108.3762]

  433. P.A.R. Ade et al. [Planck Collaboration], Planck 2013 results. XXII. Constraints on inflation. Astron. Astrophys. 571, A22 (2014). [arXiv:1303.5082]

  434. C. Germani, A. Kehagias, New model of inflation with nonminimal derivative coupling of Standard Model Higgs boson to gravity. Phys. Rev. Lett. 105, 011302 (2010). [arXiv:1003.2635]

  435. C. Germani, A. Kehagias, Cosmological perturbations in the new Higgs inflation. JCAP 1005, 019 (2010); Erratum-ibid. 1006, E01 (2010). [arXiv:1003.4285]

  436. G.F. Giudice, H.M. Lee, Unitarizing Higgs inflation. Phys. Lett. B 694, 294 (2011). [arXiv:1010.1417]

  437. R.N. Lerner, J. McDonald, Unitarity-violation in generalized Higgs inflation models. JCAP 1211, 019 (2012). [arXiv:1112.0954]

  438. R.N. Lerner, J. McDonald, Unitarity-conserving Higgs inflation model. Phys. Rev. D 82, 103525 (2010). [arXiv:1005.2978]

  439. K. Nakayama, F. Takahashi, Higgs chaotic inflation in standard model and NMSSM. JCAP 1102, 010 (2011). [arXiv:1008.4457]

  440. K. Kamada, T. Kobayashi, M. Yamaguchi, J.’i. Yokoyama, Higgs G-inflation. Phys. Rev. D 83, 083515 (2011). [arXiv:1012.4238]

  441. J. Wess, B. Zumino, Supergauge transformations in four dimensions. Nucl. Phys. B 70, 39 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  442. J. Wess, B. Zumino, A Lagrangian model invariant under supergauge transformations. Phys. Lett. B 49, 52 (1974)

    Article  ADS  Google Scholar 

  443. A. Salam, J.A. Strathdee, Supergauge transformations. Nucl. Phys. B 76, 477 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  444. S. Ferrara, J. Wess, B. Zumino, Supergauge multiplets and superfields. Phys. Lett. B 51, 239 (1974)

    Article  ADS  Google Scholar 

  445. J.D. Lykken, Introduction to supersymmetry. arXiv:hep-th/9612114

  446. E. Cremmer, J. Scherk, The supersymmetric non-linear σ-model in four dimensions and its coupling to supergravity. Phys. Lett. B 74, 341 (1978)

    Article  ADS  Google Scholar 

  447. B. Zumino, Supersymmetry and Kähler manifolds. Phys. Lett. B 87, 203 (1979)

    Article  ADS  Google Scholar 

  448. R.L. Arnowitt, P. Nath, B. Zumino, Superfield densities and action principle in curved superspace. Phys. Lett. B 56, 81 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  449. D.Z. Freedman, P. van Nieuwenhuizen, S. Ferrara, Progress toward a theory of supergravity. Phys. Rev. D 13, 3214 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  450. S. Deser, B. Zumino, Consistent supergravity. Phys. Lett. B 62, 335 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  451. E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Ferrara, L. Girardello, Super-Higgs effect in supergravity with general scalar interactions. Phys. Lett. B 79, 231 (1978)

    Article  ADS  Google Scholar 

  452. E. Cremmer, B. Julia, J. Scherk, S. Ferrara, L. Girardello, P. van Nieuwenhuizen, Spontaneous symmetry breaking and Higgs effect in supergravity without cosmological constant. Nucl. Phys. B 147, 105 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  453. R. Barbieri, S. Ferrara, D.V. Nanopoulos, K.S. Stelle, Supergravity, R invariance and spontaneous supersymmetry breaking. Phys. Lett. B 113, 219 (1982)

    Google Scholar 

  454. E. Witten, J. Bagger, Quantization of Newton’s constant in certain supergravity theories. Phys. Lett. B 115, 202 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  455. J. Wess, J. Bagger, Supersymmetry and Supergravity (Princeton University Press, Princeton, 1992)

    MATH  Google Scholar 

  456. J. Wess, B. Zumino, Superspace formulation of supergravity. Phys. Lett. B 66, 361 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  457. J. Wess, B. Zumino, Superfield Lagrangian for supergravity. Phys. Lett. B 74, 51 (1978)

    Article  ADS  Google Scholar 

  458. M. Müller, The density multiplet in superspace. Z. Phys. C 16, 41 (1982)

    Article  ADS  Google Scholar 

  459. N.-P. Chang, S. Ouvry, X. Wu, N = 1 supergravity with nonminimal coupling: a class of models. Phys. Rev. Lett. 51, 327 (1983)

  460. E. Cremmer, S. Ferrara, L. Girardello, A. Van Proeyen, Coupling supersymmetric Yang–Mills theories to supergravity. Phys. Lett. B 116, 231 (1982)

    Article  ADS  Google Scholar 

  461. E. Cremmer, S. Ferrara, L. Girardello, A. Van Proeyen, Yang–Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect. Nucl. Phys. B 212, 413 (1983)

    Article  ADS  Google Scholar 

  462. J.A. Bagger, Coupling the gauge-invariant supersymmetric non-linear sigma model to supergravity. Nucl. Phys. B 211, 302 (1983)

    Article  ADS  Google Scholar 

  463. E.D. Stewart, Inflation, supergravity, and superstrings. Phys. Rev. D 51, 6847, (1995). [arXiv:hep-ph/9405389]

  464. D.V. Nanopoulos, K.A. Olive, M. Srednicki, K. Tamvakis, Primordial inflation in simple supergravity. Phys. Lett. B 123, 41 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  465. G.B. Gelmini, D.V. Nanopoulos, K.A. Olive, Finite temperature effects in primordial inflation. Phys. Lett. B 131, 53 (1983)

    Article  ADS  Google Scholar 

  466. A.D. Linde, Primordial inflation without primordial monopoles. Phys. Lett. B 132, 317 (1983)

    Article  ADS  Google Scholar 

  467. B.A. Ovrut, P.J. Steinhardt, Supersymmetry and inflation: a new approach. Phys. Lett. B 133, 161 (1983)

    Article  ADS  Google Scholar 

  468. R. Holman, P. Ramond, G.G. Ross, Supersymmetric inflationary cosmology. Phys. Lett. B 137, 343 (1984)

    Article  ADS  Google Scholar 

  469. B.A. Ovrut, P.J. Steinhardt, Inflationary cosmology and the mass hierarchy in locally supersymmetric theories. Phys. Rev. Lett. 53, 732 (1984)

    Article  ADS  Google Scholar 

  470. E. Cremmer, S. Ferrara, C. Kounnas, D.V. Nanopoulos, Naturally vanishing cosmological constant in N = 1 supergravity. Phys. Lett. B 133, 61 (1983)

  471. J.R. Ellis, A.B. Lahanas, D.V. Nanopoulos, K. Tamvakis, No-scale supersymmetric standard model. Phys. Lett. B 134, 429 (1984)

    Article  ADS  Google Scholar 

  472. J.R. Ellis, C. Kounnas, D.V. Nanopoulos, Phenomenological SU(1, 1) supergravity. Nucl. Phys. B 241, 406 (1984)

  473. J.R. Ellis, C. Kounnas, D.V. Nanopoulos, No-scale supersymmetric GUTs. Nucl. Phys. B 247, 373 (1984)

    Article  ADS  Google Scholar 

  474. J.R. Ellis, C. Kounnas, D.V. Nanopoulos, No-scale supergravity models with a Planck mass gravitino. Phys. Lett. B 143, 410 (1984)

    Article  ADS  Google Scholar 

  475. N. Dragon, M.G. Schmidt, U. Ellwanger, Sliding scales in minimal supergravity. Phys. Lett. B 145, 192 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  476. R. Barbieri, E. Cremmer, S. Ferrara, Flat and positive potentials in N = 1 supergravity. Phys. Lett. B 163, 143 (1985)

  477. A.B. Lahanas, D.V. Nanopoulos, The road to no-scale supergravity. Phys. Rep. 145, 1 (1987)

    Article  ADS  Google Scholar 

  478. G. Gelmini, C. Kounnas, D.V. Nanopoulos, Primordial inflation with flat supergravity potentials. Nucl. Phys. B 250, 177 (1985)

    Article  ADS  Google Scholar 

  479. A.S. Goncharov, A.D. Linde, A simple realisation of the inflationary Universe scenario in SU(1, 1) supergravity. Class. Quantum Grav. 1, L75 (1984)

  480. J.R. Ellis, K. Enqvist, D.V. Nanopoulos, K.A. Olive, M. Srednicki, SU(N,1) inflation. Phys. Lett. B 152, 175 (1985); Erratum-ibid. B 156, 452 (1985)

  481. H. Murayama, H. Suzuki, T. Yanagida, J. Yokoyama, Chaotic inflation and baryogenesis in supergravity. Phys. Rev. D 50, 2356 (1994). [arXiv:hep-ph/9311326]

  482. M. Kawasaki, M. Yamaguchi, T. Yanagida, Natural chaotic inflation in supergravity. Phys. Rev. Lett. 85, 3572 (2000). [arXiv:hep-ph/0004243]

  483. R. Kallosh, A. Linde, New models of chaotic inflation in supergravity. JCAP 1011, 011 (2010). [arXiv:1008.3375]

  484. D. Croon, J. Ellis, N.E. Mavromatos, Wess–Zumino inflation in light of Planck. Phys. Lett. B 724, 165 (2013). [arXiv:1303.6253]

  485. K. Nakayama, F. Takahashi, T.T. Yanagida, Polynomial chaotic inflation in the Planck era. Phys. Lett. B 725, 111 (2013). [arXiv:1303.7315]

  486. M. Kawasaki, M. Yamaguchi, Supersymmetric topological inflation model. Phys. Rev. D 65, 103518 (2002). [arXiv:hep-ph/0112093]

  487. M.B. Einhorn, D.R.T. Jones, Inflation with non-minimal gravitational couplings in supergravity. JHEP 1003, 026 (2010). [arXiv:0912.2718]

  488. S. Ferrara, R. Kallosh, A. Linde, A. Marrani, A. Van Proeyen, Jordan frame supergravity and inflation in the NMSSM. Phys. Rev. D 82, 045003 (2010). [arXiv:1004.0712]

  489. H.M. Lee, Chaotic inflation in Jordan frame supergravity. JCAP 1008, 003 (2010). [arXiv:1005.2735]

  490. S. Ferrara, R. Kallosh, A. Linde, A. Marrani, A. Van Proeyen, Superconformal symmetry, NMSSM, and inflation. Phys. Rev. D 83, 025008 (2011). [arXiv:1008.2942]

  491. I. Ben-Dayan, M.B. Einhorn, Supergravity Higgs inflation and shift symmetry in electroweak theory. JCAP 1012, 002 (2010). [arXiv:1009.2276]

  492. K. Nakayama, F. Takahashi, General analysis of inflation in the Jordan frame supergravity. JCAP 1011, 039 (2010). [arXiv:1009.3399]

  493. M. Arai, S. Kawai, N. Okada, Higgs inflation in minimal supersymmetric SU(5) GUT. Phys. Rev. D 84, 123515 (2011). [arXiv:1107.4767]

  494. R. Kallosh, A. Linde, Superconformal generalization of the chaotic inflation model \(\frac{\lambda }{4}\phi ^{4} - \frac{\xi } {2}\phi ^{2}R\). JCAP 1306, 027 (2013). [arXiv:1306.3211]

  495. R. Kallosh, A. Linde, Universality class in conformal inflation. JCAP 1307, 002 (2013). [arXiv:1306.5220]

  496. A.A. Starobinsky, A new type of isotropic cosmological models without singularity. Phys. Lett. B 91, 99 (1980)

    Article  ADS  Google Scholar 

  497. V.F. Mukhanov, G.V. Chibisov, Quantum fluctuation and nonsingular universe. Pis’ma Zh. Eksp. Teor. Fiz. 33, 549 (1981) [JETP Lett. 33, 532 (1981)]

  498. J.D. Barrow, A.C. Ottewill, The stability of general relativistic cosmological theory. J. Phys. A 16, 2757 (1983)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  499. A.A. Starobinskiĭ, The perturbation spectrum evolving from a nonsingular initially de Sitter cosmology and the microwave background anisotropy. Pis’ma Astron. Zh. 9, 579 (1983) [Sov. Astron. Lett. 9, 302 (1983)]

  500. B. Whitt, Fourth-order gravity as general relativity plus matter. Phys. Lett. B 145, 176 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  501. L.A. Kofman, A.D. Linde, A.A. Starobinsky, Inflationary universe generated by the combined action of a scalar field and gravitational vacuum polarization. Phys. Lett. B 157, 361 (1985)

    Article  ADS  Google Scholar 

  502. A.A. Starobinsky, H.-J. Schmidt, On a general vacuum solution of fourth-order gravity. Class. Quantum Grav. 4, 695 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  503. K.-i. Maeda, Inflation as a transient attractor in R 2 cosmology. Phys. Rev. D 37, 858 (1988)

    Article  ADS  Google Scholar 

  504. K.-i. Maeda, J.A. Stein-Schabes, T. Futamase, Inflation in a renormalizable cosmological model and the cosmic no-hair conjecture. Phys. Rev. D 39, 2848 (1989)

    Article  ADS  Google Scholar 

  505. J. Ellis, D.V. Nanopoulos, K.A. Olive, No-scale supergravity realization of the Starobinsky model of inflation. Phys. Rev. Lett. 111, 111301 (2013); Erratum-ibid. 111, 129902 (2013). [arXiv:1305.1247]

  506. J. Ellis, D.V. Nanopoulos, K.A. Olive, Starobinsky-like inflationary models as avatars of no-scale supergravity. JCAP 1310, 009 (2013). [arXiv:1307.3537]

  507. S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. Phys. Lett. B 190, 86 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  508. S. Cecotti, S. Ferrara, M. Porrati, S. Sabharwal, New minimal higher derivative supergravity coupled to matter. Nucl. Phys. B 306, 160 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  509. R. Kallosh, A. Linde, Superconformal generalizations of the Starobinsky model. JCAP 1306, 028 (2013). [arXiv:1306.3214]

  510. J.A. Casas, Baryogenesis, inflation and superstrings, in International Europhysics Conference on High Energy Physics, ed. by D. Lellouch, G. Mikenberg, E. Rabinovici (Springer, Berlin, 1999). [arXiv:hep-ph/9802210]

  511. J. Ellis, M.A.G. García, D.V. Nanopoulos, K.A. Olive, A no-scale inflationary model to fit them all. JCAP 1408, 044 (2014). [arXiv:1405.0271]

  512. J. Ellis, M.A.G. García, D.V. Nanopoulos, K.A. Olive, Two-field analysis of no-scale supergravity inflation. JCAP 1501, 010 (2015). [arXiv:1409.8197]

  513. J. Ellis, M.A.G. García, D.V. Nanopoulos, K.A. Olive, Phenomenological aspects of no-scale inflation models. JCAP 1510, 003 (2015). [arXiv:1503.08867]

  514. W. Buchmuller, V. Domcke, K. Kamada, The Starobinsky model from superconformal D-term inflation. Phys. Lett. B 726, 467 (2013). [arXiv:1306.3471]

  515. F. Farakos, A. Kehagias, A. Riotto, On the Starobinsky model of inflation from supergravity. Nucl. Phys. B 876, 187 (2013). [arXiv:1307.1137]

  516. S.V. Ketov, A.A. Starobinsky, Embedding R + R 2 inflation in supergravity. Phys. Rev. D 83, 063512 (2011). [arXiv:1011.0240]

  517. S.V. Ketov, A.A. Starobinsky, Inflation and non-minimal scalar-curvature coupling in gravity and supergravity. JCAP 1208, 022 (2012). [arXiv:1203.0805]

  518. A.S. Goncharov, A.D. Linde, Chaotic inflation of the universe in supergravity. Zh. Eksp. Teor. Fiz. 86, 1594 (1984) [JETP 59, 930 (1984)]

  519. A.S. Goncharov, A.D. Linde, Chaotic inflation in supergravity. Phys. Lett. B 139, 27 (1984)

    Article  ADS  Google Scholar 

  520. R. Kallosh, A. Linde, Planck, LHC, and α-attractors. Phys. Rev. D 91, 083528 (2015). [arXiv:1502.07733]

  521. R. Kallosh, A. Linde, T. Rube, General inflaton potentials in supergravity. Phys. Rev. D 83, 043507 (2011). [arXiv:1011.5945]

  522. R. Kallosh, A. Linde, K.A. Olive, T. Rube, Chaotic inflation and supersymmetry breaking. Phys. Rev. D 84, 083519 (2011). [arXiv:1106.6025]

  523. S. Ferrara, R. Kallosh, A. Linde, M. Porrati, Minimal supergravity models of inflation. Phys. Rev. D 88, 085038 (2013). [arXiv:1307.7696]

  524. R. Kallosh, A. Linde, D. Roest, Superconformal inflationary α-attractors. JHEP 1311, 198 (2013). [arXiv:1311.0472]

  525. S. Cecotti, R. Kallosh, Cosmological attractor models and higher curvature supergravity. JHEP 1405, 114 (2014). [arXiv:1403.2932]

  526. R. Kallosh, A. Linde, D. Roest, Large field inflation and double α-attractors. JHEP 1408, 052 (2014). [arXiv:1405.3646]

  527. R. Kallosh, A. Linde, Escher in the sky. C. R. Phys. 16, 914 (2015). [arXiv:1503.06785]

  528. D. Roest, M. Scalisi, Cosmological attractors from α-scale supergravity. Phys. Rev. D 92, 043525 (2015). [arXiv:1503.07909]

  529. A. Linde, Single-field α-attractors. JCAP 1505, 003 (2015). [arXiv:1504.00663]

  530. J.J.M. Carrasco, R. Kallosh, A. Linde, D. Roest, Hyperbolic geometry of cosmological attractors. Phys. Rev. D 92, 041301 (2015). [arXiv:1504.05557]

  531. J.J.M. Carrasco, R. Kallosh, A. Linde, Cosmological attractors and initial conditions for inflation. Phys. Rev. D 92, 063519 (2015). [arXiv:1506.00936]

  532. J.J.M. Carrasco, R. Kallosh, A. Linde, α-attractors: Planck, LHC and dark energy. JHEP 1510, 147 (2015). [arXiv:1506.01708]

  533. J.A. Casas, C. Muñoz, Inflation from superstrings. Phys. Lett. B 216, 37 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  534. J.A. Casas, J.M. Moreno, C. Muñoz, M. Quirós, Cosmological implications of an anomalous U(1): inflation, cosmic strings and constraints on superstring parameters. Nucl. Phys. B 328, 272 (1989)

    Article  ADS  Google Scholar 

  535. P. Binetruy, G.R. Dvali, D-term inflation. Phys. Lett. B 388, 241 (1996). [arXiv:hep-ph/9606342]

  536. E. Halyo, Hybrid inflation from supergravity D-terms. Phys. Lett. B 387, 43 (1996). [arXiv:hep-ph/9606423]

  537. T. Matsuda, Successful D-term inflation with moduli. Phys. Lett. B 423, 35 (1998). [arXiv:hep-ph/9705448]

  538. G. Calcagni, Slow-roll parameters in braneworld cosmologies. Phys. Rev. D 69, 103508 (2004). [arXiv:hep-ph/0402126]

  539. G. Calcagni, S. Tsujikawa, Observational constraints on patch inflation in noncommutative spacetime. Phys. Rev. D 70, 103514 (2004). [arXiv:astro-ph/0407543]

  540. G. Calcagni, Braneworld Cosmology and Noncommutative Inflation. Ph.D. thesis, Parma University, Parma (2005). [arXiv:hep-ph/0503044]

Download references

Author information

Authors and Affiliations

  1. Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain

    Gianluca Calcagni

Authors
  1. Gianluca Calcagni
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Calcagni, G. (2017). Inflation. In: Classical and Quantum Cosmology. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-41127-9_5

Download citation

Publish with us

Policies and ethics

Search

Navigation