Inflation and Cosmological Perturbations

Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 800)

Summary

The purpose of these lectures is to give a pedagogical introduction to inflation and the production of the primordial perturbations, as well as a review of some of the latest developments in this domain.

After a short introduction, we review the main principles of the Hot Big Bang model, as well as its limitations. These deficiencies provide the motivation for the study of a cosmological phase of accelerated expansion, called inflation, which can be induced by a slow-rolling scalar field. A few illustrative models are presented. We then turn to the analysis of cosmological perturbations and explain how the vacuum quantum fluctuations are amplified during an inflationary phase. The next step consists in relating the perturbations generated during inflation to the perturbations of the cosmological fluid in the standard radiation-dominated phase. One can thus confront the predictions of inflationary models with cosmological observations, such as the measurements of the Cosmic Microwave Background or the large-scale structure surveys. The present constraints on inflationary models are discussed.

The final part of these lectures gives a review of more general models of inflation, involving multiple fields or non-standard kinetic terms. Although more complicated, these models are usually motivated by high-energy physics and they can lead to specific signatures that are not expected in the simplest models of inflation. After introducing a very general formalism to describe perturbations in multi-field models with arbitrary kinetic terms, several interesting cases are presented. We also stress the role of entropy perturbations in the context of multi-field models. Finally, we discuss in detail the non-Gaussianities of the primordial perturbations and some models that could produce a detectable level of non-Gaussianities.

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References

  1. 1.
    A. Linde, Particle Physics and Inflationary Cosmology, (Harwood, Chur, 1990).Google Scholar
  2. 2.
    A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large-Scale Structure, (Cambridge University Press, Cambridge, 2000).Google Scholar
  3. 3.
    V. Mukhanov, Physical Foundations of Cosmology, (Cambridge University Press, Cambridge 2005).MATHCrossRefGoogle Scholar
  4. 4.
    J.E. Lidsey, A.R. Liddle, E.W. Kolb, E.J. Copeland, T. Barreiro and M. Abney, Rev. Mod. Phys. 69, 373 (1997) [arXiv:astro-ph/9508078].CrossRefADSGoogle Scholar
  5. 5.
    D.H. Lyth and A. Riotto, Phys. Rept. 314, 1 (1998) [hep-ph/9807278].CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    A. Riotto, arXiv:hep-ph/0210162.Google Scholar
  7. 7.
    D. Langlois, “Inflation, quantum fluctuations and cosmological perturbations,” in Cargese 2003, Particle Physics and Cosmology, pp. 235–278 [arXiv:hep-th/0405053].Google Scholar
  8. 8.
    B.A. Bassett, S. Tsujikawa and D. Wands, Rev. Mod. Phys. 78, 537 (2006) [arXiv:astro-ph/0507632].CrossRefADSGoogle Scholar
  9. 9.
    D. Langlois, Prog. Theor. Phys. Suppl. 163, 258 (2006) [arXiv:hep-th/0509231].CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    A.R. Liddle and S.M. Leach, Phys. Rev. D 68, 103503 (2003) [arXiv:astro-ph/0305263].CrossRefADSGoogle Scholar
  11. 11.
    A.D. Linde, Phys. Rev. D 49, 748 (1994) [arXiv:astro-ph/9307002].CrossRefADSGoogle Scholar
  12. 12.
    A.H. Guth, Phys. Rev. D 23, 347 (1981).CrossRefADSGoogle Scholar
  13. 13.
    A.A. Starobinsky, Phys. Lett. B 91, 99 (1980).CrossRefADSGoogle Scholar
  14. 14.
    A.D. Linde, Phys. Lett. B 108, 389 (1982).CrossRefMathSciNetADSGoogle Scholar
  15. 15.
    A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982).CrossRefADSGoogle Scholar
  16. 16.
    A.D. Linde, Phys. Lett. B 129, 177 (1983).CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    L. McAllister and E. Silverstein, Gen. Rel. Grav. 40, 565 (2008) [arXiv:0710.2951 [hep-th]].MATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    C.P. Burgess, PoS P2GC (2006) 008 [Class. Quant. Grav. 24, S795 (2007)] [arXiv:0708.2865 [hep-th]].Google Scholar
  19. 19.
    R. Kallosh, On Inflation in String Theory. Lect. Notes Phys. 738 119 (2008) [arXiv:hep-th/0702059].CrossRefADSGoogle Scholar
  20. 20.
    J.M. Cline, arXiv:hep-th/0612129.Google Scholar
  21. 21.
    S.H. Henry Tye, Brane Inflation: String Theory Viewed from the Cosmos. Lect. Notes Phys. 737, 949 (2008) [arXiv:hep-th/0610221].CrossRefADSGoogle Scholar
  22. 22.
    V.F. Mukhanov and G. V. Chibisov, JETP Lett. 33, 532 (1981) [Pisma Zh. Eksp. Teor. Fiz. 33, 549 (1981)].Google Scholar
  23. 23.
    A.H. Guth and S. Y. Pi, Phys. Rev. Lett. 49, 1110 (1982).CrossRefADSGoogle Scholar
  24. 24.
    A.A. Starobinsky, Phys. Lett. B 117, 175 (1982).CrossRefADSGoogle Scholar
  25. 25.
    S.W. Hawking, Phys. Lett. B 115, 295 (1982).CrossRefADSGoogle Scholar
  26. 26.
    V.F. Mukhanov, JETP Lett. 41, 493 (1985) [Pisma Zh. Eksp. Teor. Fiz. 41, 402 (1985)].Google Scholar
  27. 27.
    V. F. Mukhanov, Sov. Phys. JETP 67, 1297 (1988) [Zh. Eksp. Teor. Fiz. 94N7, 1 (1988)].Google Scholar
  28. 28.
    J.M. Bardeen, Phys. Rev. D 22, 1882 (1980).CrossRefMathSciNetADSGoogle Scholar
  29. 29.
    H. Kodama and M. Sasaki, Prog. Theor. Phys. Suppl. 78, 1 (1984).CrossRefADSGoogle Scholar
  30. 30.
    V.F. Mukhanov, H. A. Feldman and R. H. Brandenberger, Phys. Rept. 215, 203 (1992).CrossRefMathSciNetADSGoogle Scholar
  31. 31.
    K.A. Malik and D. Wands, Phys. Rept. 475, 1 (2009) [arXiv:0809.4944 [astro-ph]].CrossRefMathSciNetADSGoogle Scholar
  32. 32.
    M. Sasaki, Prog. Theor. Phys. 76, 1036 (1986).CrossRefADSGoogle Scholar
  33. 33.
    D. Langlois, Class. Quant. Grav. 11, 389 (1994).CrossRefMathSciNetADSGoogle Scholar
  34. 34.
    S. Anderegg and V. F. Mukhanov, Phys. Lett. B 331, 30 (1994) [arXiv:hep-th/9403091].CrossRefADSGoogle Scholar
  35. 35.
    J.M. Maldacena, JHEP 0305, 013 (2003) [arXiv:astro-ph/0210603].CrossRefADSGoogle Scholar
  36. 36.
    R. Arnowitt, S. Deser, C.W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962) [arXiv:gr-qc/0405109]Google Scholar
  37. 37.
    A.A. Starobinsky, JETP Lett. 30, 682 (1979) [Pisma Zh. Eksp. Teor. Fiz. 30, 719 (1979)].Google Scholar
  38. 38.
    G.F.R. Ellis and M. Bruni, Phys. Rev. D 40, 1804 (1989).CrossRefMathSciNetADSGoogle Scholar
  39. 39.
    D. Langlois and F. Vernizzi, Phys. Rev. Lett. 95, 091303 (2005) [arXiv:astro-ph/0503416].CrossRefMathSciNetADSGoogle Scholar
  40. 40.
    D. Langlois and F. Vernizzi, Phys. Rev. D 72, 103501 (2005) [arXiv:astro-ph/0509078].CrossRefADSGoogle Scholar
  41. 41.
    D. Langlois and F. Vernizzi, JCAP 0602, 014 (2006) [arXiv:astro-ph/0601271].ADSGoogle Scholar
  42. 42.
    D.H. Lyth, K. A. Malik and M. Sasaki, JCAP 0505, 004 (2005) [arXiv:astro-ph/0411220].ADSGoogle Scholar
  43. 43.
    G.I. Rigopoulos and E. P. S. Shellard, Phys. Rev. D 68, 123518 (2003) [arXiv:astro-ph/0306620].CrossRefMathSciNetADSGoogle Scholar
  44. 44.
    J.M. Bardeen, P. J. Steinhardt and M. S. Turner, Phys. Rev. D 28, 679 (1983).CrossRefADSGoogle Scholar
  45. 45.
    D. Wands, K. A. Malik, D. H. Lyth and A. R. Liddle, Phys. Rev. D 62, 043527 (2000) [arXiv:astro-ph/0003278].CrossRefMathSciNetADSGoogle Scholar
  46. 46.
    J. Martin and R. H. Brandenberger, Phys. Rev. D 63, 123501 (2001) [arXiv:hep-th/0005209].CrossRefADSGoogle Scholar
  47. 47.
    S. Weinberg, Phys. Rev. D 70, 043541 (2004) [arXiv:astro-ph/0401313].CrossRefMathSciNetADSGoogle Scholar
  48. 48.
    R. Durrer, The Cosmic Microwave Background, (Cambridge University Press, Cambridge, UK, 2008).Google Scholar
  49. 49.
    A. Challinor and H. Peiris, AIP Conf. Proc. 1132, 86 (2009) [arXiv:0903.5158 [astro-ph.CO]].CrossRefADSGoogle Scholar
  50. 50.
    D.H. Lyth, Phys. Rev. Lett. 78, 1861 (1997) [arXiv:hep-ph/9606387].CrossRefADSGoogle Scholar
  51. 51.
    D. Langlois, S. Renaux-Petel, D. A. Steer and T. Tanaka, Phys. Rev. D 78, 063523 (2008) [arXiv:0806.0336 [hep-th]].CrossRefADSGoogle Scholar
  52. 52.
    M. Sasaki and E.D. Stewart, Prog. Theor. Phys. 95, 71 (1996) [arXiv:astro-ph/9507001];CrossRefADSGoogle Scholar
  53. 53.
    S. Groot Nibbelink and B. J. W. van Tent, Class. Quant. Grav. 19, 613 (2002) [arXiv:hep-ph/0107272].MATHCrossRefADSGoogle Scholar
  54. 54.
    D. Langlois and S. Renaux-Petel, JCAP 0804, 017 (2008) [arXiv:0801.1085 [hep-th]].ADSGoogle Scholar
  55. 55.
    C. Gordon, D. Wands, B. A. Bassett and R. Maartens, Phys. Rev. D 63, 023506 (2001) [arXiv:astro-ph/0009131].CrossRefADSGoogle Scholar
  56. 56.
    F. Di Marco, F. Finelli and R. Brandenberger, Phys. Rev. D 67, 063512 (2003) [arXiv:astro-ph/0211276].CrossRefADSGoogle Scholar
  57. 57.
    Z. Lalak, D. Langlois, S. Pokorski and K. Turzynski, JCAP 0707, 014 (2007) [arXiv:0704.0212 [hep-th]].ADSGoogle Scholar
  58. 58.
    D. Langlois and F. Vernizzi, JCAP 0702, 017 (2007) [arXiv:astro-ph/0610064].ADSGoogle Scholar
  59. 59.
    S. Renaux-Petel and G. Tasinato, JCAP 0901, 012 (2009) [arXiv:0810.2405 [hep-th]].ADSGoogle Scholar
  60. 60.
    G.I. Rigopoulos, E.P.S. Shellard and B.J.W. van Tent, Phys. Rev. D 73, 083521 (2006) [arXiv:astro-ph/0504508].CrossRefADSGoogle Scholar
  61. 61.
    M. Sasaki and T. Tanaka, Prog. Theor. Phys. 99, 763 (1998) [arXiv:gr-qc/9801017].CrossRefADSGoogle Scholar
  62. 62.
    A.A. Starobinsky and J. Yokoyama, “Density fluctuations in Brans-Dicke inflation”, gr-qc/9502002Google Scholar
  63. 63.
    D. Langlois, Phys. Rev. D 59, 123512 (1999) [arXiv:astro-ph/9906080].CrossRefADSGoogle Scholar
  64. 64.
    C. Armendariz-Picon, T. Damour and V. F. Mukhanov, Phys. Lett. B 458, 209 (1999) [arXiv:hep-th/9904075].MATHCrossRefMathSciNetADSGoogle Scholar
  65. 65.
    J. Garriga and V.F. Mukhanov, Phys. Lett. B 458, 219 (1999) [arXiv:hep-th/9904176].MATHCrossRefMathSciNetADSGoogle Scholar
  66. 66.
    D. Langlois, S. Renaux-Petel and D.A. Steer, JCAP 0904, 021 (2009) [arXiv:0902.2941 [hep-th]].ADSGoogle Scholar
  67. 67.
    E. Silverstein and D. Tong, Phys. Rev. D 70, 103505 (2004) [arXiv:hep-th/0310221];CrossRefMathSciNetADSGoogle Scholar
  68. 68.
    M. Alishahiha, E. Silverstein and D. Tong, Phys. Rev. D 70, 123505 (2004) [arXiv:hep-th/0404084].CrossRefADSGoogle Scholar
  69. 69.
    D. Langlois, S. Renaux-Petel, D. A. Steer and T. Tanaka, Phys. Rev. Lett. 101, 061301 (2008) [arXiv:0804.3139 [hep-th]].CrossRefADSGoogle Scholar
  70. 70.
    N. Bartolo, S. Matarrese and A. Riotto, Phys. Rev. D 64, 123504 (2001) [arXiv:astro-ph/0107502].CrossRefADSGoogle Scholar
  71. 71.
    K. Enqvist and M. S. Sloth, Nucl. Phys. B 626, 395 (2002) [arXiv:hep-ph/0109214];CrossRefADSGoogle Scholar
  72. 72.
    D. H. Lyth and D. Wands, Phys. Lett. B 524, 5 (2002) [arXiv:hep-ph/0110002];MATHCrossRefADSGoogle Scholar
  73. 73.
    T. Moroi and T. Takahashi, Phys. Lett. B 522, 215 (2001) [Erratum-ibid. B 539, 303 (2002)] [arXiv:hep-ph/0110096].Google Scholar
  74. 74.
    A.D. Linde and V.F. Mukhanov, Phys. Rev. D 56, 535 (1997) [arXiv:astro-ph/9610219].CrossRefADSGoogle Scholar
  75. 75.
    D. Langlois and F. Vernizzi, Phys. Rev. D 70, 063522 (2004) [arXiv:astro-ph/0403258].CrossRefADSGoogle Scholar
  76. 76.
    D.H. Lyth, C. Ungarelli and D. Wands, Phys. Rev. D 67, 023503 (2003) [arXiv:astro-ph/0208055].CrossRefADSGoogle Scholar
  77. 77.
    G. Dvali, A. Gruzinov and M. Zaldarriaga, Phys. Rev. D 69, 023505 (2004) [arXiv:astro-ph/0303591].CrossRefADSGoogle Scholar
  78. 78.
    L. Kofman, arXiv:astro-ph/0303614.Google Scholar
  79. 79.
    G. Dvali, A. Gruzinov and M. Zaldarriaga, Phys. Rev. D 69, 083505 (2004) [arXiv:astro-ph/0305548].CrossRefADSGoogle Scholar
  80. 80.
    F. Vernizzi, Phys. Rev. D 69, 083526 (2004) [arXiv:astro-ph/0311167].CrossRefMathSciNetADSGoogle Scholar
  81. 81.
    D. Langlois and L. Sorbo, arXiv:0906.1813 [astro-ph.CO].Google Scholar
  82. 82.
    D. J. H. Chung, E. W. Kolb, A. Riotto and I. I. Tkachev, Phys. Rev. D 62, 043508 (2000) [arXiv:hep-ph/9910437].CrossRefADSGoogle Scholar
  83. 83.
    D. Langlois and A. Riazuelo, Phys. Rev. D 62, 043504 (2000) [arXiv:astro-ph/9912497].CrossRefADSGoogle Scholar
  84. 84.
    E. Komatsu et al. [WMAP Collaboration], arXiv:0803.0547 [astro-ph].Google Scholar
  85. 85.
    N. Bartolo, E. Komatsu, S. Matarrese and A. Riotto, Phys. Rept. 402, 103 (2004) [arXiv:astro-ph/0406398].CrossRefMathSciNetADSGoogle Scholar
  86. 86.
    V. Acquaviva, N. Bartolo, S. Matarrese and A. Riotto, Nucl. Phys. B 667, 119 (2003) [arXiv:astro-ph/0209156].MATHCrossRefADSGoogle Scholar
  87. 87.
    E. Komatsu and D.N. Spergel, Phys. Rev. D 63, 063002 (2001) [arXiv:astro-ph/0005036].CrossRefADSGoogle Scholar
  88. 88.
    D. Babich, P. Creminelli and M. Zaldarriaga, JCAP 0408, 009 (2004) [arXiv:astro-ph/0405356].ADSGoogle Scholar
  89. 89.
    A. A. Starobinsky, JETP Lett. 42, 152 (1985) [Pisma Zh. Eksp. Teor. Fiz. 42, 124 (1985)].Google Scholar
  90. 90.
    D. H. Lyth and Y. Rodriguez, Phys. Rev. Lett. 95, 121302 (2005) [arXiv:astro-ph/0504045].CrossRefADSGoogle Scholar
  91. 91.
    D. Seery and J.E. Lidsey, JCAP 0509, 011 (2005) [arXiv:astro-ph/0506056].ADSGoogle Scholar
  92. 92.
    P. Creminelli, JCAP 0310, 003 (2003) [arXiv:astro-ph/0306122].MathSciNetADSGoogle Scholar
  93. 93.
    D. Seery and J.E. Lidsey, JCAP 0506, 003 (2005) [arXiv:astro-ph/0503692].ADSGoogle Scholar
  94. 94.
    X. Chen, M. x. Huang, S. Kachru and G. Shiu, JCAP 0701, 002 (2007) [arXiv:hep-th/0605045].ADSGoogle Scholar
  95. 95.
    D. Seery, J.E. Lidsey and M.S. Sloth, JCAP 0701, 027 (2007) [arXiv:astro-ph/0610210].ADSGoogle Scholar
  96. 96.
    C.T. Byrnes, M. Sasaki and D. Wands, Phys. Rev. D 74, 123519 (2006) [arXiv:astro-ph/0611075].CrossRefADSGoogle Scholar
  97. 97.
    F. Vernizzi and D. Wands, JCAP 0605, 019 (2006) [arXiv:astro-ph/0603799].ADSGoogle Scholar
  98. 98.
    F. Bernardeau and J.P. Uzan, Phys. Rev. D 67, 121301 (2003) [arXiv:astro-ph/0209330].CrossRefADSGoogle Scholar
  99. 99.
    M. Sasaki, Prog. Theor. Phys. 120, 159 (2008) [arXiv:0805.0974 [astro-ph]].MATHCrossRefADSGoogle Scholar
  100. 100.
    N. Bartolo, S. Matarrese and A. Riotto, JCAP 0401, 003 (2004) [arXiv:astro-ph/0309692].ADSGoogle Scholar
  101. 101.
    K. Ichikawa, T. Suyama, T. Takahashi and M. Yamaguchi, Phys. Rev. D 78, 023513 (2008) [arXiv:0802.4138 [astro-ph]].CrossRefADSGoogle Scholar
  102. 102.
    M. Sasaki, J. Valiviita and D. Wands, Phys. Rev. D 74, 103003 (2006) [arXiv:astro-ph/0607627].CrossRefADSGoogle Scholar
  103. 103.
    M. Kawasaki, K. Nakayama, T. Sekiguchi, T. Suyama and F. Takahashi, JCAP 0811, 019 (2008) [arXiv:0808.0009 [astro-ph]].ADSGoogle Scholar
  104. 104.
    D. Langlois, F. Vernizzi and D. Wands, JCAP 0812, 004 (2008) [arXiv:0809.4646 [astro-ph]].ADSGoogle Scholar
  105. 105.
    M. Kawasaki, K. Nakayama, T. Sekiguchi, T. Suyama and F. Takahashi, JCAP 0901, 042 (2009) [arXiv:0810.0208 [astro-ph]].ADSGoogle Scholar
  106. 106.
    T. Moroi and T. Takahashi, Phys. Lett. B 671, 339 (2009) [arXiv:0810.0189 [hep-ph]].CrossRefADSGoogle Scholar
  107. 107.
    M. Zaldarriaga, Phys. Rev. D 69, 043508 (2004) [arXiv:astro-ph/0306006].CrossRefADSGoogle Scholar
  108. 108.
    K. Ichikawa, T. Suyama, T. Takahashi and M. Yamaguchi, Phys. Rev. D 78, 063545 (2008) [arXiv:0807.3988 [astro-ph]].CrossRefADSGoogle Scholar
  109. 109.
    S. Renaux-Petel, arXiv:0907.2476 [hep-th].Google Scholar
  110. 110.
    S. Mizuno, F. Arroja and K. Koyama, arXiv:0907.2439 [hep-th].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.APC (CNRS-Université Paris 7)Paris Cedex 13France

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