Symmetries for generating string cosmologies

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 58, Issue 4, 1998, Pages 435031-4350311

  Copeland, E J ^a   Lidsey, James E ^a,b   Wands, David ^c  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b Mathematical Sciences   (United Kingdom)

^c UNIVERSITY OF PORTSMOUTH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0542446515     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.58.043503     Document Type: Article

References (68)

1. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
2. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
3. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
4. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
5. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
6. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
7. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
8. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
9. A. Sen, Int. J. Mod. Phys. A 9, 3707 (1994); E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, Nucl. Phys. B (Proc. Suppl.) 41, 1 (1995); E. Witten, Nucl. Phys. B443, 85 (1995); A. Sen, Nucl. Phys. B (Proc. Suppl.) 58, 5 (1997); J. Polchinski, Rev. Mod. Phys. 68, 1245 (1996); M. Duff, Int. J. Mod. Phys. A 11, 5623 (1996); P. S. Aspinwall, Nucl. Phys. B (Proc. Suppl.) 46, 30 (1996); J. H. Schwarz, ibid. 55, 1 (1997); C. Vafa, "Lectures on Strings and Dualities," hep-th/9702201.
10. A. Giveon, M. Porrati, and E. Rabinovici, Phys. Rep. 244, 77 (1994).
11. C. Hull and P. Townsend, Nucl. Phys. B438, 109 (1995).
12. C. M. Hull, Nucl. Phys. B468, 113 (1996).
13. C. Vafa, Nucl. Phys. B469, 403 (1996).
14. J. Dai, R. G. Leigh, and J. Polchinski, Mod. Phys. Lett. A 4, 2073 (1989); M. Dine, P. Huet, and N. Seiberg, Nucl. Phys. B322, 301 (1989).
15. J. Dai, R. G. Leigh, and J. Polchinski, Mod. Phys. Lett. A 4, 2073 (1989); M. Dine, P. Huet, and N. Seiberg, Nucl. Phys. B322, 301 (1989).
16. E. Cremmer and B. Julia, Phys. Lett. 80B, 48 (1978); Nucl. Phys. B159, 141 (1979).
17. E. Cremmer and B. Julia, Phys. Lett. 80B, 48 (1978); Nucl. Phys. B159, 141 (1979).
18. K. A. Meissner and G. Veneziano, Phys. Lett. B 267, 33 (1991).
19. J. Maharana and J. Schwarz, Nucl. Phys. B390, 3 (1993).
20. M. Gasperini, J. Maharana, and G. Veneziano, Phys. Lett. B 296, 51 (1992).
21. M. Gasperini, J. Maharana, and G. Veneziano, Phys. Lett. B 272, 277 (1991).
22. A. Shapere, S. Trivedi, and F. Wilczek, Mod. Phys. Lett. A 6, 2677 (1991); A. Sen, ibid. 8, 2023 (1993).
23. A. Shapere, S. Trivedi, and F. Wilczek, Mod. Phys. Lett. A 6, 2677 (1991); A. Sen, ibid. 8, 2023 (1993).
24. E. J. Copeland, A. Lahiri, and D. Wands, Phys. Rev. D 50, 4868 (1994).
25. N. Kaloper, Phys. Rev. D 55, 3394 (1997).
26. E. J. Copeland, R. Easther, and D. Wands, Phys. Rev. D 56, 874 (1997).
27. E. J. Copeland, J. E. Lidsey, and D. Wands, Nucl. Phys. B506, 407 (1997).
28. E. J. Copeland, J. E. Lidsey, and D. Wands, Phys. Rev. D 57, 625 (1998).
29. R. Poppe and S. Schwager, Phys. Lett. B 393, 51 (1997).
30. A. Feinstein, R. Lazkoz, and M. A. Vazquez-Mozo, Phys. Rev. D 56, 5166 (1997).
31. J. H. Schwarz, Nucl. Phys. B226, 269 (1984); P. Howe and P. C. West, ibid. B238, 181 (1984).
32. J. H. Schwarz, Nucl. Phys. B226, 269 (1984); P. Howe and P. C. West, ibid. B238, 181 (1984).
33. N. Marcus and J. H. Schwarz, Phys. Lett. 115B, 111 (1982).
34. E. Bergshoeff, C. Hull, and T. Ortin, Nucl. Phys. B451, 547 (1995).
35. J. H. Schwarz, Phys. Lett. B 360, 13 (1995); 364, 252 (1995); E. Bergshoeff and H. J. Boonstra, Phys. Rev. D 53, 7206 (1996).
36. J. H. Schwarz, Phys. Lett. B 360, 13 (1995); 364, 252 (1995); E. Bergshoeff and H. J. Boonstra, Phys. Rev. D 53, 7206 (1996).
37. J. H. Schwarz, Phys. Lett. B 360, 13 (1995); 364, 252 (1995); E. Bergshoeff and H. J. Boonstra, Phys. Rev. D 53, 7206 (1996).
38. J. Maharana, Phys. Lett. B 402, 64 (1997).
39. S. Roy, "On the S-duality of toroidally compactified type IIB string effective action," hep-th/9705016.
40. E. Bergshoeff, H. J. Boonstra, and T. Ortin, Phys. Rev. D 53, 7206 (1996).
41. A. Andrianopoli, R. D'Auria, S. Ferrara, P. Fre, R. Minasian, and M. Trigiante, Nucl. Phys. B493, 249 (1997).
42. E. J. Copeland, A. Lahiri, and D. Wands, Phys. Rev. D 51, 1569 (1995).
43. D. V. Gal'tsov, A. A. Garcia, and O. V. Kechkin, Class. Quantum Grav. 12, 2887 (1995).
44. D. Maison, Gen. Relativ. Gravit. 10, 717 (1979).
45. A. Lukas, B. A. Ovrut, and D. Waldram, Nucl. Phys. B509, 169 (1998).
46. G. F. R. Ellis and M. A. H. MacCallum, Commun. Math. Phys. 12, 108 (1969).
47. J. Wainwright and G. F. R. Ellis, Dynamical Systems in Cosmology (Cambridge University Press, Cambridge, England, 1997).
48. A. H. Taub, Ann. Math. 53, 472 (1951).
49. J. P. Mimoso and D. Wands, Phys. Rev. D 52, 5612 (1995).
50. A. Lukas, B. A. Ovrut, and D. Waldram, Phys. Lett. B 393, 65 (1997); Nucl. Phys. B495, 365 (1997); A. Lukas and B. A. Ovrut, "U-duality covariant M-theory cosmology," hep-th/9709030.
51. A. Lukas, B. A. Ovrut, and D. Waldram, Phys. Lett. B 393, 65 (1997); Nucl. Phys. B495, 365 (1997); A. Lukas and B. A. Ovrut, "U-duality covariant M-theory cosmology," hep-th/9709030.
52. A. Lukas, B. A. Ovrut, and D. Waldram, Phys. Lett. B 393, 65 (1997); Nucl. Phys. B495, 365 (1997); A. Lukas and B. A. Ovrut, "U-duality covariant M-theory cosmology," hep-th/9709030.
53. H. Lü, S. Mukherji, and C. N. Pope, Phys. Rev. D 55, 7926 (1997); H. Lü, J. Maharana, S. Mukherji, and C. N. Pope, ibid. 57, 2219 (1998).
54. H. Lü, S. Mukherji, and C. N. Pope, Phys. Rev. D 55, 7926 (1997); H. Lü, J. Maharana, S. Mukherji, and C. N. Pope, ibid. 57, 2219 (1998).
55. B. Kostant, Adv. Math, 34, 195 (1979).
56. M. Gasperini and G. Veneziano, Astropart. Phys. 1, 317 (1993).
57. N. A. Batakis and A. A. Kehagias, Nucl. Phys. B449, 248 (1995); N. A. Batakis, Phys. Lett. B 353, 39 (1995); 353, 450 (1995); N. A. Batakis and A. A. Kehagias, ibid. 356, 223 (1995); J. D. Barrow and M. P, Dabrowski, Phys. Rev. D 55, 630 (1997).
58. N. A. Batakis and A. A. Kehagias, Nucl. Phys. B449, 248 (1995); N. A. Batakis, Phys. Lett. B 353, 39 (1995); 353, 450 (1995); N. A. Batakis and A. A. Kehagias, ibid. 356, 223 (1995); J. D. Barrow and M. P, Dabrowski, Phys. Rev. D 55, 630 (1997).
59. N. A. Batakis and A. A. Kehagias, Nucl. Phys. B449, 248 (1995); N. A. Batakis, Phys. Lett. B 353, 39 (1995); 353, 450 (1995); N. A. Batakis and A. A. Kehagias, ibid. 356, 223 (1995); J. D. Barrow and M. P, Dabrowski, Phys. Rev. D 55, 630 (1997).
60. N. A. Batakis and A. A. Kehagias, Nucl. Phys. B449, 248 (1995); N. A. Batakis, Phys. Lett. B 353, 39 (1995); 353, 450 (1995); N. A. Batakis and A. A. Kehagias, ibid. 356, 223 (1995); J. D. Barrow and M. P, Dabrowski, Phys. Rev. D 55, 630 (1997).
61. N. A. Batakis and A. A. Kehagias, Nucl. Phys. B449, 248 (1995); N. A. Batakis, Phys. Lett. B 353, 39 (1995); 353, 450 (1995); N. A. Batakis and A. A. Kehagias, ibid. 356, 223 (1995); J. D. Barrow and M. P, Dabrowski, Phys. Rev. D 55, 630 (1997).
62. A. Strominger, Nucl. Phys. B343, 167 (1990); E. Bergshoeff, H. J. Boonstra, and T. Ortin, Phys. Rev. D 53, 7206 (1996).
63. A. Strominger, Nucl. Phys. B343, 167 (1990); E. Bergshoeff, H. J. Boonstra, and T. Ortin, Phys. Rev. D 53, 7206 (1996).
64. J. D. Barrow and K. E. Kunze, Phys. Rev. D 55, 623 (1997).
65. E. Verdager, Phys. Rep. 229, 1 (1993).
66. I. Bakas, Nucl. Phys. B428, 374 (1994).
67. S. Kar, A. Kumar, and G. Sengupta, Phys, Lett. B 375, 121 (1996).
68. J. B. Griffiths, Colliding Plane Waves in General Relativity (Clarendon, Oxford, 1991).