Advertisement

G-bounce inflation: towards nonsingular inflation cosmology with galileon field

Open Access
Regular Article - Theoretical Physics

Abstract

We study a nonsingular bounce inflation model, which can drive the early universe from a contracting phase, bounce into an ordinary inflationary phase, followed by the reheating process. Besides the bounce that avoided the Big-Bang singularity which appears in the standard cosmological scenario, we make use of the Horndesky theory and design the kinetic and potential forms of the lagrangian, so that neither of the two big problems in bouncing cosmology, namely the ghost and the anisotropy problems, will appear. The cosmological perturbations can be generated either in the contracting phase or in the inflationary phase, where in the latter the power spectrum will be scale-invariant and fit the observational data, while in the former the perturbations will have nontrivial features that will be tested by the large scale structure experiments. We also fit our model to the CMB TT power spectrum.

Keywords

Classical Theories of Gravity Spacetime Singularities 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A.H. Guth, The inflationary universe: a possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].ADSMATHGoogle Scholar
  2. [2]
    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 (1982) 389 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    A. Albrecht and P.J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  5. [5]
    L.Z. Fang, Entropy generation in the early universe by dissipative processes near the Higgsphase transitions, Phys. Lett. B 95 (1980) 154 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    K. Sato, First order phase transition of a vacuum and expansion of the universe, Mon. Not. Roy. Astron. Soc. 195 (1981) 467 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S.W. Hawking and R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. Lond. A 314 (1970) 529 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge U.K. (1973).CrossRefMATHGoogle Scholar
  9. [9]
    A. Borde and A. Vilenkin, Eternal inflation and the initial singularity, Phys. Rev. Lett. 72 (1994)3305 [gr-qc/9312022] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Novello and S.E.P. Bergliaffa, Bouncing cosmologies, Phys. Rept. 463 (2008) 127 [arXiv:0802.1634] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    Y.-F. Cai, T. Qiu, Y.-S. Piao, M. Li and X. Zhang, Bouncing universe with quintom matter, JHEP 10 (2007) 071 [arXiv:0704.1090] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    Y.-F. Cai, T. Qiu, R. Brandenberger, Y.-S. Piao and X. Zhang, On perturbations of quintom bounce, JCAP 03 (2008) 013 [arXiv:0711.2187] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    Y.-F. Cai, T.-t. Qiu, J.-Q. Xia and X. Zhang, A model of inflationary cosmology without singularity, Phys. Rev. D 79 (2009) 021303 [arXiv:0808.0819] [INSPIRE].ADSGoogle Scholar
  14. [14]
    Y.-F. Cai, T.-t. Qiu, R. Brandenberger and X.-m. Zhang, A nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory, Phys. Rev. D 80 (2009) 023511 [arXiv:0810.4677] [INSPIRE].ADSGoogle Scholar
  15. [15]
    T. Qiu and K.-C. Yang, Perturbations in matter bounce with non-minimal coupling, JCAP 11 (2010) 012 [arXiv:1007.2571] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    H.-H. Xiong, T. Qiu, Y.-F. Cai and X. Zhang, Cyclic universe with quintom matter in loop quantum cosmology, Mod. Phys. Lett. A 24 (2009) 1237 [arXiv:0711.4469] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    H.-H. Xiong, Y.-F. Cai, T. Qiu, Y.-S. Piao and X. Zhang, Oscillating universe with quintom matter, Phys. Lett. B 666 (2008) 212 [arXiv:0805.0413] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    Y.-S. Piao, Can the universe experience many cycles with different vacua?, Phys. Rev. D 70 (2004) 101302 [hep-th/0407258] [INSPIRE].ADSGoogle Scholar
  19. [19]
    Y.-S. Piao, Proliferation in cycle, Phys. Lett. B 677 (2009) 1 [arXiv:0901.2644] [INSPIRE].ADSGoogle Scholar
  20. [20]
    J. Zhang, Z.-G. Liu and Y.-S. Piao, Amplification of curvature perturbations in cyclic cosmology, Phys. Rev. D 82 (2010) 123505 [arXiv:1007.2498] [INSPIRE].ADSGoogle Scholar
  21. [21]
    M. Ostrogradski, Memoires sur les equations differentielles relatives au probleme des isoperimetres, Mem. Ac. St. Petersbourg VI 4 (1850) 385.Google Scholar
  22. [22]
    R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    S.M. Carroll, M. Hoffman and M. Trodden, Can the dark energy equation-of-state parameter w be less than −1?, Phys. Rev. D 68 (2003) 023509 [astro-ph/0301273] [INSPIRE].ADSGoogle Scholar
  24. [24]
    J.M. Cline, S. Jeon and G.D. Moore, The phantom menaced: constraints on low-energy effective ghosts, Phys. Rev. D 70 (2004) 043543 [hep-ph/0311312] [INSPIRE].ADSGoogle Scholar
  25. [25]
    V.K. Onemli and R.P. Woodard, Superacceleration from massless, minimally coupled ϕ 4, Class. Quant. Grav. 19 (2002) 4607 [gr-qc/0204065] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  26. [26]
    V.K. Onemli and R.P. Woodard, Quantum effects can render w → −1 on cosmological scales, Phys. Rev. D 70 (2004) 107301 [gr-qc/0406098] [INSPIRE].ADSGoogle Scholar
  27. [27]
    E.O. Kahya and V.K. Onemli, Quantum stability of a w → −1 phase of cosmic acceleration, Phys. Rev. D 76 (2007) 043512 [gr-qc/0612026] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].ADSMathSciNetGoogle Scholar
  29. [29]
    C. Deffayet, G. Esposito-Farese and A. Vikman, Covariant Galileon, Phys. Rev. D 79 (2009) 084003 [arXiv:0901.1314] [INSPIRE].ADSGoogle Scholar
  30. [30]
    A. Nicolis, R. Rattazzi and E. Trincherini, Energys and amplitudespositivity, JHEP 05 (2010) 095 [Erratum ibid. 1111 (2011) 128] [arXiv:0912.4258] [INSPIRE].
  31. [31]
    C. Deffayet, S. Deser and G. Esposito-Farese, Generalized Galileons: all scalar models whose curved background extensions maintain second-order field equations and stress-tensors, Phys. Rev. D 80 (2009) 064015 [arXiv:0906.1967] [INSPIRE].ADSGoogle Scholar
  32. [32]
    C. Deffayet, X. Gao, D.A. Steer and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev. D 84 (2011) 064039 [arXiv:1103.3260] [INSPIRE].ADSGoogle Scholar
  33. [33]
    G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].MathSciNetCrossRefGoogle Scholar
  34. [34]
    T. Qiu, J. Evslin, Y.-F. Cai, M. Li and X. Zhang, Bouncing galileon cosmologies, JCAP 10 (2011) 036 [arXiv:1108.0593] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    D.A. Easson, I. Sawicki and A. Vikman, G-bounce, JCAP 11 (2011) 021 [arXiv:1109.1047] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    T. Qiu, X. Gao and E.N. Saridakis, Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations, Phys. Rev. D 88 (2013) 043525 [arXiv:1303.2372] [INSPIRE].ADSGoogle Scholar
  37. [37]
    K.E. Kunze and R. Durrer, Anisotropichairsin string cosmology, Class. Quant. Grav. 17 (2000) 2597 [gr-qc/9912081] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [38]
    J.K. Erickson, D.H. Wesley, P.J. Steinhardt and N. Turok, Kasner and mixmaster behavior in universes with equation of state w → 1, Phys. Rev. D 69 (2004) 063514 [hep-th/0312009] [INSPIRE].ADSMathSciNetGoogle Scholar
  39. [39]
    B. Xue and P.J. Steinhardt, Unstable growth of curvature perturbation in non-singular bouncing cosmologies, Phys. Rev. Lett. 105 (2010) 261301 [arXiv:1007.2875] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    B. Xue and P.J. Steinhardt, Evolution of curvature and anisotropy near a nonsingular bounce, Phys. Rev. D 84 (2011) 083520 [arXiv:1106.1416] [INSPIRE].ADSGoogle Scholar
  41. [41]
    Y.-S. Piao, B. Feng and X.-m. Zhang, Suppressing CMB quadrupole with a bounce from contracting phase to inflation, Phys. Rev. D 69 (2004) 103520 [hep-th/0310206] [INSPIRE].ADSGoogle Scholar
  42. [42]
    Y.-S. Piao, A possible explanation to low CMB quadrupole, Phys. Rev. D 71 (2005) 087301 [astro-ph/0502343] [INSPIRE].ADSGoogle Scholar
  43. [43]
    Y.-S. Piao, S. Tsujikawa and X.-m. Zhang, Inflation in string inspired cosmology and suppression of CMB low multipoles, Class. Quant. Grav. 21 (2004) 4455 [hep-th/0312139] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  44. [44]
    T. Qiu, Galileon bouncing inflation after BICEP2, arXiv:1404.3060 [INSPIRE].
  45. [45]
    Z.-G. Liu, Z.-K. Guo and Y.-S. Piao, Obtaining the CMB anomalies with a bounce from the contracting phase to inflation, Phys. Rev. D 88 (2013) 063539 [arXiv:1304.6527] [INSPIRE].ADSGoogle Scholar
  46. [46]
    Y.-T. Wang and Y.-S. Piao, Parity violation in pre-inflationary bounce, Phys. Lett. B 741 (2015)55 [arXiv:1409.7153] [INSPIRE].CrossRefMATHGoogle Scholar
  47. [47]
    J.-Q. Xia, Y.-F. Cai, H. Li and X. Zhang, Evidence for bouncing evolution before inflation after BICEP2, Phys. Rev. Lett. 112 (2014) 251301 [arXiv:1403.7623] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    Y. Cai, Y.-T. Wang and Y.-S. Piao, Pre-inflationary primordial perturbations, arXiv:1501.01730 [INSPIRE].
  49. [49]
    Y.-F. Cai, D.A. Easson and R. Brandenberger, Towards a nonsingular bouncing cosmology, JCAP 08 (2012) 020 [arXiv:1206.2382] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    M. Koehn, J.-L. Lehners and B.A. Ovrut, Cosmological super-bounce, Phys. Rev. D 90 (2014) 025005 [arXiv:1310.7577] [INSPIRE].ADSGoogle Scholar
  51. [51]
    L. Battarra, M. Koehn, J.-L. Lehners and B.A. Ovrut, Cosmological perturbations through a non-singular ghost-condensate/galileon bounce, JCAP 07 (2014) 007 [arXiv:1404.5067] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok, The ekpyrotic universe: colliding branes and the origin of the hot Big Bang, Phys. Rev. D 64 (2001) 123522 [hep-th/0103239] [INSPIRE].ADSMathSciNetGoogle Scholar
  53. [53]
    J. Khoury, B.A. Ovrut, N. Seiberg, P.J. Steinhardt and N. Turok, From Big Crunch to Big Bang, Phys. Rev. D 65 (2002) 086007 [hep-th/0108187] [INSPIRE].ADSGoogle Scholar
  54. [54]
    J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok, Density perturbations in the ekpyrotic scenario, Phys. Rev. D 66 (2002) 046005 [hep-th/0109050] [INSPIRE].ADSMathSciNetGoogle Scholar
  55. [55]
    A. Fertig, J.-L. Lehners and E. Mallwitz, Ekpyrotic perturbations with small non-gaussian corrections, Phys. Rev. D 89 (2014) 103537 [arXiv:1310.8133] [INSPIRE].ADSGoogle Scholar
  56. [56]
    A. Ijjas, J.-L. Lehners and P.J. Steinhardt, General mechanism for producing scale-invariant perturbations and small non-Gaussianity in ekpyrotic models, Phys. Rev. D 89 (2014) 123520 [arXiv:1404.1265] [INSPIRE].ADSGoogle Scholar
  57. [57]
    K.A. Olive, Inflation, Phys. Rept. 190 (1990) 307 [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, Astron. Astrophys. 571 (2014) A22 [arXiv:1303.5082] [INSPIRE].CrossRefGoogle Scholar
  59. [59]
    X.-F. Zhang and T. Qiu, Avoiding the big-rip jeopardy in a quintom dark energy model with higher derivatives, Phys. Lett. B 642 (2006) 187 [astro-ph/0603824] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    T. Kobayashi, M. Yamaguchi and J. Yokoyama, G-inflation: inflation driven by the Galileon field, Phys. Rev. Lett. 105 (2010) 231302 [arXiv:1008.0603] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    A. De Felice and S. Tsujikawa, Inflationary non-Gaussianities in the most general second-order scalar-tensor theories, Phys. Rev. D 84 (2011) 083504 [arXiv:1107.3917] [INSPIRE].ADSGoogle Scholar
  62. [62]
    V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rept. 215 (1992) 203 [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    J.-c. Hwang and E.T. Vishniac, Gauge-invariant joining conditions for cosmological perturbations, Astrophys. J. 382 (1991) 363 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  64. [64]
    N. Deruelle and V.F. Mukhanov, On matching conditions for cosmological perturbations, Phys. Rev. D 52 (1995) 5549 [gr-qc/9503050] [INSPIRE].ADSGoogle Scholar
  65. [65]
    S. Nishi, T. Kobayashi, N. Tanahashi and M. Yamaguchi, Cosmological matching conditionsand galilean genesis in Horndeskis theory, JCAP 03 (2014) 008 [arXiv:1401.1045] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    D. Pirtskhalava, L. Santoni, E. Trincherini and P. Uttayarat, Inflation from Minkowski space, JHEP 12 (2014) 151 [arXiv:1410.0882] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  67. [67]
    BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    B.A. Bassett, S. Tsujikawa and D. Wands, Inflation dynamics and reheating, Rev. Mod. Phys. 78 (2006) 537 [astro-ph/0507632] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Institute of AstrophysicsCentral China Normal UniversityWuhanChina
  2. 2.State Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  3. 3.School of PhysicsUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations