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Nonminimal Couplings in the Early Universe: Multifield Models of Inflation and the Latest Observations

  • David I. KaiserEmail author
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 183)

Abstract

Models of cosmic inflation suggest that our universe underwent an early phase of accelerated expansion, driven by the dynamics of one or more scalar fields. Inflationary models make specific, quantitative predictions for several observable quantities, including particular patterns of temperature anistropies in the cosmic microwave background radiation. Realistic models of high-energy physics include many scalar fields at high energies. Moreover, we may expect these fields to have nonminimal couplings to the spacetime curvature. Such couplings are quite generic, arising as renormalization counterterms when quantizing scalar fields in curved spacetime. In this chapter I review recent research on a general class of multifield inflationary models with nonminimal couplings. Models in this class exhibit a strong attractor behavior: across a wide range of couplings and initial conditions, the fields evolve along a single-field trajectory for most of inflation. Across large regions of phase space and parameter space, therefore, models in this general class yield robust predictions for observable quantities that fall squarely within the “sweet spot” of recent observations.

Keywords

Scalar Field Cosmic Microwave Background Background Field Einstein Frame Jordan Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

It is a great pleasure to thank Carl Brans for his kind encouragement over the years. I would also like to thank Torsten Asselmeyer-Maluga for editing this Festschrift in honor of Carl’s 80th birthday. I am indebted to Evangelos Sfakianakis for pursuing the research reviewed here with me, along with our collaborators Matthew DeCross, Ross Greenwood, Edward Mazenc, Audrey (Todhunter) Mithani, Anirudh Prabhu, Chanda Prescod-Weinstein, and Katelin Schutz. This research has also benefited from discussions with Bruce Bassett and Alan Guth over the years. This work was conducted in MIT’s Center for Theoretical Physics and supported in part by the U.S. Department of Energy under grant Contract Number DE-SC0012567.

References

  1. 1.
    C. H. Brans, Mach’s principle and a varying gravitational constant. Ph.D. dissertation, Princeton University, 1961Google Scholar
  2. 2.
    C.H. Brans, R.H. Dicke, Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925 (1961)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    C.H. Brans, Mach’s principle and a relativistic theory of gravitation, II. Phys. Rev. 125, 2194 (1962); C.H. Brans, Mach’s principle and the locally measured gravitational constant in general relativity. Phys. Rev. 125, 388 (1962)Google Scholar
  4. 4.
    C. Will, Was Einstein Right? Putting General Relativity to the Test, 2nd ed. (Basic Books, New York, 1993 [1986])Google Scholar
  5. 5.
    J.D. Norton, Einstein, Nordström, and the early demise of Lorentz-covariant, scalar theories of gravitation. Arch. Hist. Exact Sci. 45, 17 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    D.I. Kaiser, When fields collide. Sci. Am. 296, 62 (2007)CrossRefGoogle Scholar
  7. 7.
    C.H. Brans, Varying Newton’s constant: a personal history of scalar-tensor theories. Einstein Online 04, 1002 (2010)Google Scholar
  8. 8.
    H. Goenner, Some remarks on the genesis of scalar-tensor theories. Gen. Rel. Grav. 44, 2077 (2012). arXiv:1204.3455 [gr-qc]Google Scholar
  9. 9.
    M. Janssen, Of pots and holes: Einstein’s bumpy road to general relativity. Ann. Phys. (Leipzig) 14(Supplement), 58 (2005)Google Scholar
  10. 10.
    Y. Fujii, K.-I. Maeda, The Scalar-Tensor Theory of Gravitation (Cambridge University Press, New York, 2003)zbMATHGoogle Scholar
  11. 11.
    V. Faraoni, Cosmology in Scalar-Tensor Gravity (Springer, New York, 2004)CrossRefzbMATHGoogle Scholar
  12. 12.
    S. Capozziello, V. Faraoni, Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics (Springer, New York, 2011)zbMATHGoogle Scholar
  13. 13.
    S. Nojiri, S.D. Odintsov, Unified cosmic history in modified gravity: from \(F(R)\) theory to Lorentz non-invariant models. Phys. Rep. 505, 59 (2011). arXiv:1011.0544 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    C.G. Callan Jr., S.R. Coleman, R. Jackiw, A new improved energy-momentum tensor. Annals Phys. 59, 42 (1970)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    T.S. Bunch, P. Panangaden, L. Parker, On renormalization of \(\lambda \phi ^4\) field theory in curved spacetime, I. J. Phys. A 13, 901 (1980); T.S. Bunch, P. Panangaden, On renormalization of \(\lambda \phi ^4\) field theory in curved spacetime, II. J. Phys. A 13, 919 (1980)Google Scholar
  16. 16.
    N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, New York, 1982)CrossRefzbMATHGoogle Scholar
  17. 17.
    S.D. Odintsov, Renormalization group, effective action and Grand Unification Theories in curved spacetime. Fortsh. Phys. 39, 621 (1991)MathSciNetCrossRefGoogle Scholar
  18. 18.
    I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity (Taylor and Francis, New York, 1992)Google Scholar
  19. 19.
    L.E. Parker, D.J. Toms, Quantum Field Theory in Curved Spacetime (Cambridge University Press, New York, 2009)CrossRefzbMATHGoogle Scholar
  20. 20.
    T. Markkanen, A. Tranberg, A simple method for one-loop renormalization in curved spacetime. J. Cosmol. Astropart. Phys. 08, 045 (2013). arXiv:1303.0180 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    A.H. Guth, The inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347 (1981); 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); A. Albrecht, P.J. Steinhardt, Cosmology for Grand Unified Theories with radiatively induced symmetry breaking. Phys. Rev. Lett. 48, 1220 (1982)Google Scholar
  22. 22.
    B.A. Bassett, S. Tsujikawa, D. Wands, Inflation dynamics and reheating. Rev. Mod. Phys. 78, 537 (2006). arXiv:astro-ph/0507632 ADSCrossRefGoogle Scholar
  23. 23.
    A.H. Guth, D.I. Kaiser, Inflationary cosmology: exploring the universe from the smallest to the largest scales. Science 307, 884 (2005). arXiv:astro-ph/0502328; D.H. Lyth, A.R. Liddle, The Primordial Density Perturbation: Cosmology, Inflation, and the Origin of Structure (Cambridge University Press, New York, 2009); D. Baumann, TASI Lectures on Inflation. arXiv:0907.5424 [hep-th]; J. Martin, C. Ringeval, V. Vennin, Encyclopedia inflationaris. arXiv:1303.3787 [astro-ph.CO]; A.H. Guth, D.I. Kaiser, Y. Nomura, Inflationary paradigm after Planck 2013. Phys. Lett. B 733, 112 (2014). arXiv:1312.7619 [astro-ph.CO]; A.D. Linde, Inflationary cosmology after Planck 2013. arXiv:1402.0526 [hep-th]
  24. 24.
    B.L. Spokoiny, Inflation and generation of perturbations in broken-symmetric theory of gravity. Phys. Lett. B 147, 39 (1984); F.S. Accetta, D.J. Zoller, M.S. Turner, Induced-gravity inflation. Phys. Rev. D 31, 3046 (1985); F. Lucchin, S. Matarrese, M.D. Pollock, Inflation with a nonminimally coupled scalar field. Phys. Lett. B 167, 163 (1986); R. Fakir, W.G. Unruh, Induced-gravity inflation. Phys. Rev. D 41, 1792 (1990); D.I. Kaiser, Constraints in the context of induced-gravity inflation. Phys. Rev. D 49, 6347 (1994). arXiv:astro-ph/9308043; D.I. Kaiser, Induced-gravity inflation and the density perturbation spectrum. Phys. Lett. B 340, 23 (1994). arXiv:astro-ph/9405029; J.L. Cervantes-Code, H. Dehnen, Induced gravity inflation in the Standard Model of particle physics. Nucl. Phys. B 442, 391 (1995). arXiv:astro-ph/9505069
  25. 25.
    L. Smolin, Towards a theory of spacetime structure at very short distances. Nucl. Phys. B 160, 253 (1979)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    A. Zee, Broken-symmetric theory of gravity. Phys. Rev. Lett. 42, 417 (1979)ADSCrossRefGoogle Scholar
  27. 27.
    D. La, P.J. Steinhardt, Extended inflationary cosmology. Phys. Rev. Lett. 62, 376 (1989); P.J. Steinhardt, F.S. Accetta, Hyperextended inflation. Phys. Rev. Lett. 64, 2740 (1990); R. Holman, E. W. Kolb, Y. Wang, Gravitational couplings of the inflaton in extended inflation. Phys. Rev. Lett. 65, 17 (1990); R. Holman, E.W. Kolb, S.L. Vadas, Y. Wang, Extended inflation from higher-dimensional theories. Phys. Rev. D 42, 995 (1991)Google Scholar
  28. 28.
    T. Futamase, K. Maeda, Chaotic inflationary scenario of the universe with a nonminimally coupled ‘inflaton’ field. Phys. Rev. D 39, 399 (1989); D.S. Salopek, J.R. Bond, J.M. Bardeen, Designing density fluctuation spectra in inflation. Phys. Rev. D 40, 1753 (1989); R. Fakir, S. Habib, W.G. Unruh, Cosmological density perturbations with modified gravity. Astrophys. J. 394, 396 (1992); R. Fakir, W.G. Unruh, Improvement on cosmological chaotic inflation through nonminimal coupling. Phys. Rev. D 41, 1783 (1990); N. Makino, M. Sasaki, The density perturbation in the chaotic inflation with nonminimal coupling. Prog. Theor. Phys. 86, 103 (1991); D.I. Kaiser, Primordial spectral indices from generalized Einstein theories. Phys. Rev. D 52, 4295 (1995). arXiv:astro-ph/9408044; S. Mukaigawa, T. Muta, S.D. Odintsov, Finite Grand Unified Theories and inflation. Int. J. Mod. Phys. A 13, 2839 (1998). arXiv:hep-ph/9709299; E. Komatsu, T. Futamase, Complete constraints on a nonminimally coupled chaotic inflationary scenario from the cosmic microwave background. Phys. Rev. D 59, 064029 (1999). arXiv:astro-ph/9901127; A. Linde, M. Noorbala, A. Westphal, Observational consequences of chaotic inflation with nonminimal coupling to gravity. J. Cosmol. Astropart. Phys. 1103, 013 (2011). arXiv:1101.2652 [hep-th]
  29. 29.
    F.L. Bezrukov, M.E. Shaposhnikov, The Standard Model Higgs boson as the inflaton. Phys. Lett. B 659, 703 (2008). arXiv:0710.3755 [hep-th]ADSCrossRefGoogle Scholar
  30. 30.
    D.H. Lyth, A. Riotto, Particle physics models of inflation and the cosmological density perturbation. Phys. Rept. 314, 1 (1999). arXiv:hep-ph/9807278; A. Mazumdar, J. Rocher, Particle physics models of inflation and the curvaton scenarios. Phys. Rep. 497, 85 (2011). arXiv:1001.0993 [hep-ph]; V. Vennin, K. Koyama, D. Wands, Encyclopedia curvatonis. arXiv:1507.07575 [astro-ph.CO]Google Scholar
  31. 31.
    D.I. Kaiser, A.T. Todhunter, Primordial perturbations from multifield inflation with nonminimal couplings. Phys. Rev. D 81, 124037 (2010). arXiv:1004.3805 [astro-ph.CO]ADSCrossRefGoogle Scholar
  32. 32.
    D.I. Kaiser, E.A. Mazenc, E.I. Sfakianakis, Primordial bispectrum from multifield inflation with nonminimal couplings. Phys. Rev. D 87, 064004 (2013). arXiv:1210.7487 [astro-ph.CO]ADSCrossRefGoogle Scholar
  33. 33.
    R.N. Greenwood, D.I. Kaiser, E.I. Sfakianakis, Multifield dynamics of Higgs inflation. Phys. Rev. D 87, 044038 (2013). arXiv:1210.8190 [hep-ph]CrossRefGoogle Scholar
  34. 34.
    D.I. Kaiser, E.I. Sfakianakis, Multifield inflation after Planck: the case for nonminimal couplings. Phys. Rev. Lett. 112, 011302 (2014). arXiv:1304.0363 [astro-ph.CO]ADSCrossRefGoogle Scholar
  35. 35.
    K. Schutz, E.I. Sfakianakis, D.I. Kaiser, Multifield inflation after Planck: Isocurvature modes from nonminimal couplings. Phys. Rev. D 89, 064044 (2014). arXiv:1310.8285 [astro-ph.CO]ADSCrossRefGoogle Scholar
  36. 36.
    M.P. DeCross, D.I. Kaiser, A. Prabhu, C. Prescod-Weinstein, E.I. Sfakianakis, Preheating after multifield inflation with nonminimal couplings, I: covariant formalism and attractor behavior. arXiv:1510.08553 [hep-ph]
  37. 37.
    J. White, M. Minamitsuji, M. Sasaki, Curvature perturbation in multifield inflation with nonminimal coupling. J. Cosmol. Astropart. Phys. 07, 039 (2012). arXiv:1205.0656 [astro-ph.CO]; J. White, M. Minamitsuji, M. Sasaki, Nonlinear curvature perturbation in multifield inflation models with nonminimal coupling. J. Cosmol. Astropart. Phys. 09, 015 (2013). arXiv:1406.6186 [astro-ph.CO]; A. Yu. Kamenshchik, C.F. Steinwachs, Question of quantum equivalence between Jordan frame and Einstein frame. Phys. Rev. D 91, 084033 (2015). arXiv:1408.5769 [gr-qc]
  38. 38.
    H. Kodama, M. Sasaki, Cosmological perturbation theory. Prog. Theor. Phys. Suppl. 78, 1 (1984); V.F. Mukhanov, H.A. Feldman, R.H. Brandenberger, Theory of cosmological perturbations. Phys. Rep. 215, 203 (1992); K.A. Malik, D. Wands, Cosmological perturbations. Phys. Rep. 475, 1 (2009). arXiv:0809.4944 [astro-ph]Google Scholar
  39. 39.
    R.H. Dicke, Mach’s principle and invariance under transformation of units. Phys. Rev. 125, 2163 (1962)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    D.I. Kaiser, Conformal transformations with multiple scalar fields. Phys. Rev. D 81, 084044 (2010). arXiv:1003.1159 [gr-qc]ADSCrossRefGoogle Scholar
  41. 41.
    S.V. Ketov, Quantum Nonlinear Sigma Models (Springer, New York, 2000)CrossRefzbMATHGoogle Scholar
  42. 42.
    J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models. J. High Energy Phys. 0305, 013 (2003). arXiv:astro-ph/0210603 ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    N. Bartolo, E. Komatsu, S. Matarrese, A. Riotto, Non-Gaussianity from inflation: theory and observations. Phys. Rep. 402, 103 (2004). arXiv:astro-ph/0406398; X. Chen, Primordial non-Gaussianities from inflation models. Adv. Astron., 638979 (2010). arXiv:1002.1416 [astro-ph]Google Scholar
  44. 44.
    C. Gordon, D. Wands, B.A. Bassett, R. Maartens, Adiabatic and entropy perturbations from inflation. Phys. Rev. D 63, 023506 (2001). arXiv:astro-ph/0009131; D. Wands, N. Bartolo, S. Matarrese, A. Riotto, An observational test of two-field inflation. Class. Quant. Grav. 19, 613 (2002). arXiv:hep-ph/0205253
  45. 45.
    P.A.R. Ade et al. (Planck collaboration), Planck 2015 results, XIII: cosmological parameters. arXiv:1502.01589 [astro-ph.CO]
  46. 46.
    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; D. Wands, Multiple field inflation. Lect. Notes Phys. 738, 275 (2008). arXiv:astro-ph/0702187; D. Langlois, S. Renaux-Petel, Perturbations in generalized multifield inflation. J. Cosmol. Astropart. Phys. 0804 (2008), 017. arXiv:0801.1085 [hep-th]; C.M. Peterson, M. Tegmark, Testing multifield inflation: a geometric approach. arXiv:1111.0927 [astro-ph.CO]; J.-O. Gong, T. Tanaka, A covariant approach to general field space metric in multifield inflation. J. Cosmol. Astropart. Phys. 1103, 015 (2011). arXiv:1101.4809 [astrod-ph.CO]
  47. 47.
    R. Kallosh, A. Linde, Nonminimal inflationary attractors. J. Cosmol. Astropart. Phys. 1310, 033 (2013). arXiv:1307.7938 [hep-th]; J.J.M. Carrasco, R. Kallosh, A. Linde, Cosmological attractors and initial conditions for inflation. arXiv:1506.00936 [hep-th], and references thereinGoogle Scholar
  48. 48.
    M.A. Amin, M.P. Hertzberg, D.I. Kaiser, J. Karouby, Nonperturbative dynamics of reheating after inflation: a review. Int. J. Mod. Phys. D 24, 1530003 (2015). arXiv:1410.3808 [hep-ph]ADSCrossRefzbMATHGoogle Scholar
  49. 49.
    N. Barnaby, J. Braden, L. Kofman, Reheating the universe after multifield inflation. J. Cosmol. Astropart. Phys. 1007, 016 (2010). arXiv:1005.2196 [hep-th]; T. Battefeld, A. Eggemeier, J.T. Giblin, Jr., Enhanced preheating after multifield inflation: on the importance of being special. J. Cosmol. Astropart. Phys. 11, 062 (2012). arXiv:1209.3301 [astro-ph.CO], and references therein
  50. 50.
    C.H. Brans, Bell’s theorem does not eliminate fully causal hidden variables. Int. J. Theor. Phys. 27, 219 (1988)CrossRefGoogle Scholar
  51. 51.
    J. Gallicchio, A.S. Friedman, D.I. Kaiser, Testing Bell’s inequality with cosmic photons: closing the setting-independence loophole. Phys. Rev. Lett. 112, 110405 (2014). arXiv:1310.3288 [quant-ph]ADSCrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Physics, Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeUSA

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