Ermakov-Pinney equation in scalar field cosmologies

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 66, Issue 2, 2002, Pages 8-

  Hawkins, Rachael M ^a   Lidsey, James E ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; COSMOLOGICAL PHENOMENA; COSMOS; ENERGY; GRAVITY; MATHEMATICAL ANALYSIS; QUANTUM THEORY; TIME;

EID: 0037101379     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.66.023523     Document Type: Article

References (109)

1. A.D. Miller, Astrophys. J. Lett. 524, L1 (1999)
2. Astrophys. J. Lett.S. Hanany, 545, L5 (2000)
3. N.W. Halverson, astro-ph/0104489
4. P. de Bernardis, Astrophys. J. 564, 559 (2002).
5. A.A. Starobinsky, Phys. Lett. 91B, 99 (1980)
6. A.H. Guth, Phys. Rev. D 23, 347 (1981)
7. A. Albrecht and P.J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)
8. S.W. Hawking and I.G. Moss, Phys. Lett. 110B, 35 (1982)
9. Phys. Lett.A.D. Linde, 108B, 389 (1982)
10. Phys. Lett.A.D. Linde129B, 177 (1983).
11. A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large Scale Structure (Cambridge University Press, Cambridge, England, 2000)
12. W. Hu and S. Dodelson, astro-ph/0110414.
13. B.P. Schmidt, Astrophys. J. 507, 46 (1998)
14. A.G. Riess, Astron. J. 116, 1009 (1998).
15. S. Perlmutter, Astrophys. J. 517, 565 (1999).
16. A.H. Jaffe, Phys. Rev. Lett. 86, 3475 (2001)
17. S. Jha, astro-ph/0101521
18. R. Bean and A. Melchiorri, Phys. Rev. D 64, 123522 (2001).
19. R.R. Caldwell, R. Dave, and P.J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998)
20. L. Wang, R.R. Caldwell, J.P. Ostriker, and P.J. Steinhardt, Astrophys. J. 530, 17 (2000).
21. J. Khoury, B.A. Ovrut, P.J. Steinhardt, and N. Turok, Phys. Rev. D 64, 123522 (2001)
22. J. Khoury, B.A. Ovrut, P.J. Steinhardt, and N. Turok, hep-th/0109050.
23. V.P. Ermakov, Univ. Izv. Kiev 20, 1 (1880).
24. H.R. Lewis, J. Math. Phys. 9, 1976 (1968).
25. J.R. Ray and J.L. Reid, Phys. Lett. 71A, 317 (1979).
26. A.M. Goncharenko, Yu.A. Logvin, A.M. Samson, and P.S. Shapovalov, Opt. Commun. 81, 225 (1991)
27. A.M. Goncharenko, Yu.A. Logvin, A.M. Samson, P.S. Shapovalov, and S.I. Turovets, Phys. Lett. A 160, 138 (1991).
28. M. Shahinpoor and J.L. Nowinski, Int. J. Non-Linear Mech. 6, 193 (1971).
29. Yu.B. Gaididei, K.O. Rasmussen, and P.L. Christiansen, Phys. Rev. E 52, 2951 (1995)
30. K.O. Rasmussen, Yu.B. Gaididei, O. Bang, and P.L. Christiansen, Math. Comput. Simul. 40, 339 (1996)
31. P.L. Hansen, D. Svensek, V.A. Parsegian, and R. Podgornik, Phys. Rev. E 60, 1956 (1999).
32. F. Finelli, G.P. Vacca, and G. Venturi, Phys. Rev. D 58, 103514 (1998)
33. C. Bertoni, F. Finelli, and G. Venturi, Phys. Lett. A 237, 331 (1998)
34. F. Finelli, A. Gruppuso, and G. Venturi, Class. Quantum Grav. 16, 3923 (1999).
35. H. Rosu, P. Espinoza, and M. Reyes, Nuovo Cimento Soc. Ital. Fis., B 114, 1435 (1999).
36. W.K. Schief, C. Rogers, and A.P. Bassom, J. Phys. A 29, 903 (1996)
37. L.M. Berkovich and N.H. Rozov, Arc. Math. (BRNO) 33, 75 (1997)
38. P.B.E. Padilla, math-ph/0002005.
39. E. Pinney, Proc. Am. Math. Soc. 1, 681 (1950).
40. W.E. Milne, Phys. Rev. 35, 863 (1930).
41. M. Lutzky, Phys. Lett. 68A, 3 (1978).
42. J.E. Lidsey, Phys. Lett. B 273, 42 (1991).
43. J.D. Barrow, in Gravitation in Astrophysics, edited by B. Carter and J.B. Hartle (Plenum, New York, 1987)
44. M.J.D. Assad and J.A.S. Lima, Gen. Relativ. Gravit. 20, 527 (1988)
45. V. Faraoni, Am. J. Phys. 67, 732 (1999)
46. H.C. Rosu, Mod. Phys. Lett. A 15, 979 (2000)
47. J.A.S. Lima, astro-ph/0109215.
48. S.P. Starkovich and F.I. Cooperstock, Astrophys. J. 398, 1 (1992).
49. N.E. Maltsev, J. Math. Phys. 35, 1387 (1994).
50. B. Mielnik and M.A. Reyes, J. Phys. A 29, 6009 (1996).
51. F. Lucchin and S. Matarrese, Phys. Rev. D 32, 1316 (1985).
52. G.F.R. Ellis and M. Madsen, Class. Quantum Grav. 8, 667 (1991).
53. L.P. Grishchuk and Yu. V. Sidorav, in Fourth Seminar on Quantum Gravity, edited by M.A. Markov, V.A. Berezin, and V.P. Frolov (World Scientific, Singapore, 1988)
54. D.S. Salopek, J.R. Bond, and J.M. Bardeen, Phys. Rev. D 40, 1753 (1989)
55. A.G. Muslimov, Class. Quantum Grav. 7, 231 (1990)
56. D.S. Salopek and J.R. Bond, Phys. Rev. D 42, 3936 (1990)
57. Phys. Rev. DR. de Ritis, G. Marmo, G. Platania, C. Rubano, P. Scudellaro, and C. Stornaiolo, 42, 1091 (1990)
58. J.E. Lidsey, Class. Quantum Grav. 8, 923 (1991)
59. B.J. Carr and J.E. Lidsey, Phys. Rev. D 48, 543 (1993)
60. Phys. Rev. DJ.D. Barrow and P. Parsons, 52, 5576 (1995)
61. L.P. Chimento, V. Méndez, and N. Zuccalá, Class. Quantum Grav. 16, 3749 (1999).
62. C. Rubano and J.D. Barrow, Phys. Rev. D 64, 127301 (2001)
63. C. Rubano and P. Scudellaro, astro-ph/0103335.
64. A.A. Starobinsky, JETP Lett. 68, 757 (1998)
65. D. Huterer and M.S. Turner, Phys. Rev. D 60, 081301 (1999)
66. T. Nakamura and T. Chiba, Mon. Not. R. Astron. Soc. 306, 689 (1999)
67. T.D. Saini, S. Raychaudhury, V. Sahni, and A.A. Starobinsky, Phys. Rev. Lett. 85, 1162 (2000)
68. Phys. Rev. Lett.I. Maor, R. Brustein, and P.J. Steinhardt, 86, 6 (2001)
69. Phys. Rev. Lett.J. Weller and A. Albrecht, 86, 1939 (2001).
70. B.F. Gerke and G. Efstathiou, astro-ph/0201336
71. V. Sahni, T. Saini, A.A. Starobinsky, and U. Alam, astro-ph/0201498.
72. M. Levi et al., http://snap.lbl.gov
73. E.R. Harrison, Mon. Not. R. Astron. Soc. 137, 69 (1967).
74. C. Wetterich, Nucl. Phys. B302, 668 (1988)
75. E.J. Copeland, A.R. Liddle, and D. Wands, Phys. Rev. D 57, 4686 (1998).
76. N. Kaloper and K.A. Olive, Astropart. Phys. 1, 185 (1993).
77. P. Binetruy and M.K. Gaillard, Phys. Rev. D 34, 3069 (1986).
78. K. Freese, J.A. Frieman, and A.V. Olinto, Phys. Rev. Lett. 65, 3233 (1990)
79. J.E. Lidsey, A.R. Liddle, E.W. Kolb, E.W. Copeland, T. Barreiro, and M. Abney, Rev. Mod. Phys. 69, 373 (1997).
80. X. Wang, M. Tegmark, and M. Zaldarriaga, Phys. Rev. D 65, 123001 (2002).
81. K. Akama, hep-th/0001113
82. V.A. Rubakov and M.E. Shaposhnikov, Phys. Lett. 159B, 22 (1985)
83. N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett. B 429, 263 (1998)
84. M. Gogberashvili, Europhys. Lett. 49, 396 (2000).
85. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999)
86. Phys. Rev. Lett.L. RandallR. Sundrum83, 4690 (1999).
87. P. Kraus, J. High Energy Phys. 12, 011 (1999)
88. J. High Energy Phys.D. Ida, 09, 014 (2000).
89. H.A. Chamblin and H.S. Reall, Nucl. Phys. B562, 133 (1999)
90. H.A. Chamblin, M.J. Perry, and H.S. Reall, J. High Energy Phys. 09, 014 (1999).
91. C. Barcelo and M. Visser, Phys. Lett. B 482, 183 (2000).
92. W. Israel, Nuovo Cimento B 44, 1 (1966).
93. P. Binétruy, C. Deffayet, U. Ellwanger, and D. Langlois, Phys. Lett. B 477, 285 (2000)
94. E.E. Flanagan, S.-H. Tye, and I. Wasserman, Phys. Rev. D 62, 044039 (2000).
95. C. Csaki, M. Graesser, C. Kolda, and J. Terning, Phys. Lett. B 462, 34 (1999)
96. J.M. Cline, C. Grojean, and G. Servant, Phys. Rev. Lett. 83, 4245 (1999)
97. S. Mukohyama, Phys. Lett. B 473, 241 (2000).
98. C. Csaki, J. Erlich, and C. Grojean, Nucl. Phys. B604, 312 (2001).
99. R.M. Hawkins and J.E. Lidsey, Phys. Rev. D 63, 041301(R) (2001).
100. K. Maeda, Phys. Rev. D 64, 123525 (2001)
101. Phys. Rev. DS. Mizuno and K. Maeda, 64, 123521 (2001).
102. C. Brans and R.H. Dicke, Phys. Rev. 124, 925 (1961)
103. P.G. Bergmann, Int. J. Theor. Phys. 1, 25 (1968)
104. R.V. Wagoner, Phys. Rev. D 1, 3209 (1970)
105. K. Nordtvedt, Astrophys. J. 161, 1059 (1970).
106. J.E. Lidsey, D. Wands, and E.J. Copeland, Phys. Rep. 337, 346 (2000).
107. J. Magueijo, Phys. Rev. D 62, 103521 (2000)
108. H. Sandvik, J.D. Barrow, and J. Magueijo, Phys. Rev. Lett. 88, 031302 (2002).
109. J.K. Webb, Phys. Rev. Lett. 87, 091301 (2001).