Cosmological perturbation theory, instantaneous gauges, and local inertial frames

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 76, Issue 6, 2007, Pages

  Bičák, Jiří ^a,b   Katz, Joseph ^c   Lynden Bell, Donald ^d  

^a CHARLES UNIVERSITY   (Czech Republic)

^b ALBERT EINSTEIN INSTITUT   (Germany)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548590888     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.76.063501     Document Type: Article

References (71)

1. C. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973).
2. C.L. Bennett, Astrophys. J. Suppl. Ser. 148, 1 (2003); APJSA2 0067-0049 10.1086/377253
3. D.N. Spergel, Astrophys. J. Suppl. Ser. 148, 175 (2003). APJSA2 0067-0049 10.1086/377226
4. These are two of 13 companion papers on first-year WMAP results. The first gives preliminary maps and basic results; the second is concerned with the determination of cosmological parameters. The three-year results [see D.N. Spergel, Astrophys. J. Suppl. Ser. APJSA2 0067-0049 170, 377 (2007)] did not change the determination of the total mass-energy density parameter of the universe. 10.1086/513700
5. S. Weinberg, Gravitation and Cosmology (John Wiley, New York, 1972).
6. G. Efstathiou, Mon. Not. R. Astron. Soc. 343, L95 (2003). Here it is shown that models with a positive spatial curvature can explain the low cosmic microwave background quadrupole measured with the WMAP. MNRAA4 0035-8711 10.1046/j.1365-8711.2003.06940.x
7. G.F.R. Ellis, W. Stoeger, P. McEwan, and P. Dunsby, Gen. Relativ. Gravit. GRGVA8 0001-7701 34, 1445 (2002). 10.1023/A:1020087004012
8. A. Lasenby and C. Doran, Phys. Rev. D 71, 063502 (2005). PRVDAQ 0556-2821 10.1103/PhysRevD.71.063502
9. G.F.R. Ellis and R. Maartens, Classical Quantum Gravity CQGRDG 0264-9381 21, 223 (2004); 10.1088/0264-9381/21/1/015
10. see also G.F.R. Ellis, J. Murugan, and G.G. Tsagas, Classical Quantum Gravity CQGRDG 0264-9381 21, 233 (2004). 10.1088/0264-9381/21/1/016
11. Ernst Mach and the Development of Physics, edited by, V. Prosser, and, J. Folta, (Universitas Carolina Pragensis Press, Prague, 1991).
12. Mach's Principle: From Newton's Bucket to Quantum Gravity, edited by, J. Barbour, and, H. Pfister, (Birkhauser, Boston, 1995). See, in particular, the list on p. 530, and detailed discussions among experts worldwide.
13. H. Bondi and J. Samuel, Phys. Lett. A 228, 121 (1997). PYLAAG 0375-9601 10.1016/S0375-9601(97)00117-5
14. T. Doležel, in Gravitation: Following the Prague Inspiration, edited by, O. Semerák,,, J. Podolský,, and, M. Žofka, (World Scientific, Singapore-London, 2002). Various formulations of Mach's principle are summarized here, and dragging effects inside slowly rotating shells both in asymptotically flat and cosmological spacetimes are reviewed.
15. D. Lynden-Bell, J. Katz, and J. Bičák, Mon. Not. R. Astron. Soc. 272, 150 (1995); MNRAA4 0035-8711
16. D. Lynden-Bell J. Katz J. Bičák Mon. Not. R. Astron. Soc. 277, 1600(E) (1995). MNRAA4 0035-8711
17. P.J.E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993).
18. J.A. Peacock, Cosmological Physics (Cambridge University Press, Cambridge, 1999).
19. H. Bondi, Cosmology (Cambridge University Press, Cambridge, 1961).
20. J. Katz, J. Bičák, and D. Lynden-Bell, Phys. Rev. D 55, 5957 (1997). PRVDAQ 0556-2821 10.1103/PhysRevD.55.5957
21. B. Julia and S. Silva, Classical Quantum Gravity CQGRDG 0264-9381 17, 4733 (2000). 10.1088/0264-9381/17/22/312
22. B. Julia and S. Silva, Classical Quantum Gravity CQGRDG 0264-9381 15, 2173 (1998). 10.1088/0264-9381/15/8/006
23. G. Amery and E.P.S. Shellard, Phys. Rev. D 67, 083502 (2003). PRVDAQ 0556-2821 10.1103/PhysRevD.67.083502
24. B. Losic and W.G. Unruh, Phys. Rev. D 72, 123510 (2005). PRVDAQ 0556-2821 10.1103/PhysRevD.72.123510
25. L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields, Fourth Revised English Edition (Butterworth-Heinemann, Oxford, 2002).
26. H. Kodama and M. Sasaki, Prog. Theor. Phys. Suppl. 78, 1 (1984). PTPSEP 0375-9687
27. J.M. Stewart, Classical Quantum Gravity CQGRDG 0264-9381 7, 1169 (1990). 10.1088/0264-9381/7/7/013
28. V.F. Mukhanov, H.A. Feldman, and R.H. Brandenberger, Phys. Rep. 215, 203 (1992). PRPLCM 0370-1573 10.1016/0370-1573(92)90044-Z
29. R. Dürrer, Fundam. Cosm. Phys. FNCPAX 0094-5846 15, 209 (1994).
30. E. Bertschinger, in Cosmology and Large Scale Structure, edited by, R. Schaffer,,, Les Houches Session LX (Elsevier, Amsterdam, 1996).
31. K. Tomita, Prog. Theor. Phys. PTPKAV 0033-068X 47, 416 (1972); 10.1143/PTP.47.416
32. M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Classical Quantum Gravity CQGRDG 0264-9381 14, 2585 (1997); 10.1088/0264-9381/14/9/014
33. H. Noh and J. Hwang, Phys. Rev. D 69, 104011 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.69.104011
34. G.F.R. Ellis and M. Bruni, Phys. Rev. D 40, 1804 (1989). PRVDAQ 0556-2821 10.1103/PhysRevD.40.1804
35. J.M. Bardeen, Phys. Rev. D 22, 1882 (1980). PRVDAQ 0556-2821 10.1103/PhysRevD.22.1882
36. J.M. Stewart and M. Walker, Proc. R. Soc. A PRLAAZ 0080-4630 341, 49 (1974). 10.1098/rspa.1974.0172
37. J. Bičák, Proc. R. Soc. A PRLAAZ 0080-4630 371, 429 (1980). 10.1098/rspa.1980.0089
38. J. Katz, D. Lynden-Bell, and J. Bičák, Classical Quantum Gravity CQGRDG 0264-9381 15, 3177 (1998). 10.1088/0264-9381/15/10/019
39. D. Lynden-Bell, J. Bičák, and J. Katz, Ann. Phys. (N.Y.) 271, 1 (1999). APNYA6 0003-4916 10.1006/aphy.1998.5869
40. I. Ciufolini and J.A. Wheeler, Gravitation and Inertia (Princeton University Press, Princeton, 1995).
41. G.F.R. Ellis, in General Relativity and Cosmology, edited by, R.K. Sachs, (Academic Press, New York, 1971).
42. S. Bashinsky and E. Bertschinger, Phys. Rev. D 65, 123008 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.65.123008
43. J. Traschen, Phys. Rev. D 29, 1563 (1984). PRVDAQ 0556-2821 10.1103/PhysRevD.29.1563
44. J. Traschen, Phys. Rev. D 31, 283 (1985). PRVDAQ 0556-2821 10.1103/PhysRevD.31.283
45. J. Traschen and D.M. Eardley, Phys. Rev. D 34, 1665 (1986). PRVDAQ 0556-2821 10.1103/PhysRevD.34.1665
46. J. Bičák, D. Lynden-Bell, and J. Katz, Phys. Rev. D 69, 064011 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.69.064011
47. J. Bičák, D. Lynden-Bell, and J. Katz, Phys. Rev. D 69, 064012 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.69.064012
48. F.A.E. Pirani, in Brandeis 1964 Summer Institute on Theoretical Physics, Lectures on General Relativity Vol. 1 (Prentice Hall, Englewood Cliffs, NJ, 1965).
49. R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
50. K.S. Thorne and D.A. Macdonald, Mon. Not. R. Astron. Soc. 198, 339 (1982). MNRAA4 0035-8711
51. D. Bini and F. de Felice, Classical Quantum Gravity CQGRDG 0264-9381 17, 4627 (2000). 10.1088/0264-9381/17/22/303
52. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1973).
53. A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge, 2000).
54. L. Smarr and J.W. York, Phys. Rev. D 17, 1945 (1978). PRVDAQ 0556-2821 10.1103/PhysRevD.17.1945
55. P. Kraus and F. Wilczek, Nucl. Phys. NUPBBO 0550-3213 B433, 403 (1995). 10.1016/0550-3213(94)00411-7
56. J.M. Bardeen, P.J. Steinhardt, and M.S. Turner, Phys. Rev. D 28, 679 (1983). PRVDAQ 0556-2821 10.1103/PhysRevD.28.679
57. A.D. Rendall, Living Rev. Relativity 1433-8351 8, 6 (2005), http://www.livingreviews.org/lrr-2005-6.
58. L. Bombelli, W.E. Couch, and R.J. Torrence, Classical Quantum Gravity CQGRDG 0264-9381 11, 139 (1994). 10.1088/0264-9381/11/1/016
59. J. Bičák and J. Katz, Czech. J. Phys. 55, 105 (2005). CZLIA6 0011-4626 10.1007/s10582-005-0024-z
60. L. Blanchet, in Einstein's Field Equations and Their Physical Implications, edited by B.G. Schmidt, Lecture Notes in Physics Vol. 540 (Springer-Verlag, New York, 2000), pp. 225-272.
61. L.P. Eisenhart, Riemannian Geometry (Princeton University Press, Princeton, 1964).
62. J. Levin, Phys. Rep. 365, 251 (2002). PRPLCM 0370-1573 10.1016/S0370-1573(02)00018-2
63. K. Tomita, Prog. Theor. Phys. 68, 310 (1982). PTPKAV 0033-068X 10.1143/PTP.68.310
64. C. Schmid, Phys. Rev. D 74, 044031 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.74.044031
65. P.D. D'Eath, Ann. Phys. (N.Y.) 98, 237 (1976). APNYA6 0003-4916 10.1016/0003-4916(76)90246-3
66. L. Lindblom and D.R. Brill, Phys. Rev. D 10, 3151 (1974). PRVDAQ 0556-2821 10.1103/PhysRevD.10.3151
67. C. Klein, Classical Quantum Gravity CQGRDG 0264-9381 10, 1619 (1993); 10.1088/0264-9381/10/8/019
68. C. Klein Classical Quantum Gravity CQGRDG 0264-9381 11, 1539 (1994). 10.1088/0264-9381/11/6/018
69. T. Doležel, J. Bičák, and N. Deruelle, Classical Quantum Gravity CQGRDG 0264-9381 17, 2719 (2000). 10.1088/0264-9381/17/14/308
70. A. Higuchi, Classical Quantum Gravity CQGRDG 0264-9381 8, 2005 (1991); 10.1088/0264-9381/8/11/011
71. R. Camporesi and A. Higuchi, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 35, 4217 (1994). 10.1063/1.530850