Relativistic second-order perturbations of the Einstein-de Sitter universe

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 58, Issue 4, 1998, Pages 435041-4350422

  Matarrese, Sabino ^a   Mollerach, Silvia ^b,d   Bruni, Marco ^c  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF VALENCIA   (Spain)

^c SISSA   (Italy)

^d UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0542375164     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.58.043504     Document Type: Article

References (48)

1. P. J. E. Peebles, The Large Scale Structure of the Universe (Princeton University Press, Princeton, 1980).
2. E. Bertschinger, in Cosmology and Large Scale Structure, Proceedings of the Les Houches School, edited hy R. Shaeffer, J. Silk, M. Spiro, and V. Zinn-Justin (Elsevier, Netherland, 1996), Sec. LX.
3. S. Matarrese, O. Pantano, and D. Sáez, Phys. Rev. Lett. 72, 320 (1994); Mon. Not. R. Astron. Soc. 271, 513 (1994).
4. S. Matarrese, O. Pantano, and D. Sáez, Phys. Rev. Lett. 72, 320 (1994); Mon. Not. R. Astron. Soc. 271, 513 (1994).
5. S. Matarrese and D. Terranova, Mon. Not. R. Astron. Soc. 283, 400 (1996).
6. P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993).
7. P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses (Springer-Verlag, Berlin, 1992).
8. L. Kofman and D. Pogosyan, Astrophys. J. 442, 30 (1995).
9. Ya. B. Zel'dovich, Astron. Astrophys. 5, 84 (1970).
10. S. Matarrese and C. Daffara (in preparation).
11. M. Bruni, S. Matarrese, and O. Pantano, in Dynamical Systems in Cosmology, edited by G. F. R. Ellis and J. Wainwright (Cambridge University Press, Cambridge, England, 1997).
12. M. Rees and D. W. Sciama, Nature (London) 217, 511 (1968).
13. T. Pyne and S. M. Carroll, Phys. Rev. D 53, 2920 (1996).
14. S. Mollerach and S. Matarrese, Phys. Rev. D 56, 4494 (1997).
15. C.-P. Ma and E. Bertschinger, Astrophys. J. 455, 7 (1995).
16. M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Class. Quantum Grav. 14, 2585 (1997).
17. S. Sonego and M. Bruni, Commun. Math. Phys. 193, 209 (1998).
18. K. Tomita, Prog. Theor. Phys. 37, 831 (1967).
19. H. Russ, M. Morita, M. Kasai, and G. Börner, Phys. Rev. D 53, 6881 (1996).
20. D. S. Salopek, J. M. Stewart, and K. M. Croudace, Mon. Not. R. Astron. Soc. 271, 1005 (1994).
21. K. Tomita, Prog. Theor. Phys. 45, 1747 (1971); 47, 416 (1972).
22. K. Tomita, Prog. Theor. Phys. 45, 1747 (1971); 47, 416 (1972).
23. E. M. Lifshitz, J. Phys. (Moscow) 10, 116 (1946); E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963); L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975).
24. E. M. Lifshitz, J. Phys. (Moscow) 10, 116 (1946); E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963); L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975).
25. E. M. Lifshitz, J. Phys. (Moscow) 10, 116 (1946); E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963); L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975).
26. R. K. Sachs, in Relativity, Groups, and Topology, edited by C. DeWitt and B. DeWitt (Gordon and Breach, New York, 1964).
27. J. M. Stewart and M. Walker, Proc. R. Soc. London A341, 49 (1974).
28. J. M. Bardeen, Phys. Rev. D 22, 1882 (1980).
29. G. F. R. Ellis and M. Bruni, Phys. Rev. D 40, 1804 (1989).
30. J. M. Stewart, Class. Quantum Grav. 7, 1169 (1990).
31. H. Kodama and M. Sasaki, Prog. Theor. Phys. Suppl. 78, 1 (1984).
32. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Phys. Rep. 215, 203 (1992).
33. R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
34. kT̃ terms.
35. R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Class. Quantum Grav. 13, L117 (1996); Phys. Rev. Lett. 77, 4483 (1996).
36. R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Class. Quantum Grav. 13, L117 (1996); Phys. Rev. Lett. 77, 4483 (1996).
37. V. F. Mukhanov, L. R. W. Abramo, and R. H. Brandenberger, Phys. Rev. Lett. 78, 1624 (1997); L. R. W. Abramo, R. H. Brandenberger, and V. F. Mukhanov, Phys. Rev. D 56, 3248 (1997).
38. V. F. Mukhanov, L. R. W. Abramo, and R. H. Brandenberger, Phys. Rev. Lett. 78, 1624 (1997); L. R. W. Abramo, R. H. Brandenberger, and V. F. Mukhanov, Phys. Rev. D 56, 3248 (1997).
39. S. Matarrese and S. Mollerach, in Proceedings of the Spanish Relativity Meeting (ERE-96), Valencia, Spain, 1996, edited by J. A. Miralles, J. A. Morales, and D. Sáez (Editions Frontières, Paris, in press), p. 87, astro-ph/9705168.
40. For nonlinear perturbations the parametrization is not unique (see Ref. [15] for a brief discussion of this point); here we simply assume that a parametrization has been given, and we work within it.
41. R. D'Inverno, Introducing Einstein's Relativity (Oxford University Press, Oxford, 1992).
42. H. Stephani, General Relativity, 2nd ed. (Cambridge University Press, Cambridge, England, 1990).
43. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1973).
44. B. F. Schutz, Geometrical Methods of Mathematical Physics (Cambridge University Press, Cambridge, England, 1980).
45. ξ] on Z.
46. R. Geroch and L. Lindblom, J. Math. Phys. 26, 2581 (1985); E. Flanagan and R. Wald, Phys. Rev. D 54, 6233 (1996); B. F. Schutz, in Relativistic Astrophysics and Cosmology, edited by X. Fustero and E. Verdaguer (World Scientific, Singapore, 1984).
47. R. Geroch and L. Lindblom, J. Math. Phys. 26, 2581 (1985); E. Flanagan and R. Wald, Phys. Rev. D 54, 6233 (1996); B. F. Schutz, in Relativistic Astrophysics and Cosmology, edited by X. Fustero and E. Verdaguer (World Scientific, Singapore, 1984).
48. R. Geroch and L. Lindblom, J. Math. Phys. 26, 2581 (1985); E. Flanagan and R. Wald, Phys. Rev. D 54, 6233 (1996); B. F. Schutz, in Relativistic Astrophysics and Cosmology, edited by X. Fustero and E. Verdaguer (World Scientific, Singapore, 1984).