Abstract
This is a review on cosmological perturbation theory. After an introduction, it presents the problem of gauge transformation. Gauge invariant variables are introduced and the Einstein and conservation equations are written in terms of these variables. Some examples, especially perfect fluids and scalar fields are presented in detail. The generation of perturbations during inflation is studied. Lightlike geodesics and their relevance for CMB anisotropies are briefly discussed. Perturbation theory in braneworlds is also introduced.
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References
1. I. Newton, Letters from Sir Isaac Newton to Dr. Bentley, Letter I, 203ff quoted by A. Koyré, From the Classical World to the Infinite Universe, Harper and Row (New York 1958).
2. E. Lifshitz, JETP 10, 116 (1946).
3. D. Barden and C. Thomas, An Introduction to Differential Manifolds, Imperial College Press (2003).
4. J.M. Stewart and M. Walker, Proc. R. Soc. London A341, 49 (1974).
5. J. Bardeen, Phys. Rev. D22, 1882 (1980).
6. H. Kodama and M. Sasaki Prog. Theor. Phys. Suppl 78, 1 (1984).
7. R. Durrer, Fund. of Cosmic Physics 15, 209 (1994).
8. M. Bruni, P. Dunsby and G. Ellis, Astrophys. J 395, 34 (1992).
9. R. Trotta, A. Riazuelo and R. Durrer, Phys. Rev. Lett. 87, 231301 (2001).
10. M. Bucher, K. Moodley and N. Turok, Phys. Rev. D 66, 023528 (2002)
11. E. Harrison, Phys. Rev. D1 2726 (1970); Ya. B. Zel’dovich, Mont. Not. R. Astr. Soc. 160, P1 (1972).
12. V. F. Mukhanov, H. A. Feldman and R. H. Brandenberger, Phys. Rept. 215, 203 (1992).
13. R. Durrer, M. Kunz and A. Melchiorri, Phys. Rept. 364, 1 (2002).
14. R.K. Sachs and A.M. Wolfe, Astrophys. J. 147, 73 (1967).
15. M. Tegmark et al., astro-ph/0310725, (2003).
16. P.J.E. Peebles, Principles of Physical Cosmology, Princeton University Press (1993).
17. G.F. Smoot et al., Astrophys. J. 396, L1 (1992).
18. U. Pen, D. Spergel and N. Turok, Phys Rev. D 49, 692 (1994).
19. R. Durrer and Z. Zhou, Phys. Rev. D 53, 5394 (1996).
20. B. Allen et al., Phys. Rev. Lett. 79, 2624 (1997).
21. R. Durrer et al., Phys. Rev. D 59, 043511 (1999)
22. T. Kanazawa, M. Kawasaki, N. Sugiyama, and T. Yanagida, Prog. Theor. Phys. 100 1055 (1998).
23. A. Melchiorri and N. Vittorio, in: Proceedings of the NATO Advanced Study Institute 1996, Strasbourg, astro-ph/9610029, (1996).
24. H. Kodama, A. Ishibashi, and O. Seto, Phys. Rev. D 62, 064022 (2000); D. Langlois, Phys. Rev. D 62, 126012 (2000); S. Mukohyama, Phys. Rev. D 62, 084015 (2000); D. Langlois, Phys. Rev. Lett. 86, 2212 (2001); H. Bridgman, K. Malik, and D. Wands, Phys. Rev. D 65, 043502 (2002); K. Koyama and J. Soda, Phys. Rev. D 65, 023514 (2002).
25. A. Riazuelo, F. Vernizzi, D. Steer and R. Durrer, hep-th/0205220, (2002).
26. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).
27. S. Weinberg, The Quantum Theory of Fields, Vol I p62ff, Cambridge University Press (1995).
28. J. Garriga and T. Tanaka, Phys. Rev. Lett. 84, 2778 (2000).
29. R. Durrer and P. Kocian, hep-th/0305181, (2003).
30. W. Goldberger and M. Wise, Phys. Lett. B475, 275 (2000).
31. J. Lesgourges and L. Sorbo, hep-th/0310007, (2003).
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Durrer, R. 2 Cosmological Perturbation Theory. In: Papantonopoulos, E. (eds) The Physics of the Early Universe. Lecture Notes in Physics, vol 653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31535-3_2
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