Quintessential inflation without a potential

Modern Physics Letters A

Volumn 18, Issue 36, 2003, Pages 2599-2609

  González Díaz, Pedro F ^a  

^a INSTITUTO DE MATEMÁTICAS Y FÍSICA FUNDAMENTAL   (Spain)

Author keywords

Chaplygin gas; Gravitational action; Inflation; Quintessence

Indexed keywords

ARTICLE; COSMOLOGICAL PHENOMENA; ENERGY; GRAVITY; MASS; MOLECULAR MODEL; VACUUM;

EID: 3042848069     PISSN: 02177323     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217732303012155     Document Type: Article

References (58)

1. P. F. González-Díaz, Phys. Lett. B562, 1 (2003).
2. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
3. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
4. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
5. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
6. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
7. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
8. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
9. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
10. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
11. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
12. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
13. J. D. Barrow, Phys. Lett. B180, 335 (1986); B235, 40 (1990); D. Bazcia and J. Jackiw, Ann. Phys. 270, 246 (1998); A. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001); N. Bilic, G. B. Tupper and R. Viollier, ibid. B535, 17 (2001); M. C. Bento, O. Bertolami and A. A. Sen, astro-ph/0202064; J. S. Fabris, S. V. Gonzalves and P. E. de Souza, Gen. Rel. Grav. 34, 53 (2002); V. Gorini, A. Kamenshchik and U. Moschella, astro-ph/0209395; A. Dev, D. Jain and J. E. Alcaniz, astro-ph/0209379; M. Makler, S. Quinet de Oliveira and I. Waga, astro-ph/0209486; D. Carturan and F. Finelli, astro-ph/0211626; P. P. Avelino, L. M. G. Beca, J. P. M. Carvalho, C. J. A. P. Martins and P. Pinto, astro-ph/0208528, Phys. Rev. D, in press.
14. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
15. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
16. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
17. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
18. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
19. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
20. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
21. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
22. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
23. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
24. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
25. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
26. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
27. C. Wetterich, Nucl. Phys. B302, 668 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, Phys. Rev. Lett. 75, 2077 (1995); P. G. Ferreira and M. Joyce, ibid. 79, 4740 (1997); V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. A9, 373 (2000); S. M. Carroll, Living Rev. Rel. 4, 1 (2001); I. Zlatev, L. Wang and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); P. J. Steinhardt, L. Wang and I. Zlatev, Phys. Rev. D59, 123504 (1999); I. Zlatev and P. J. Steinhardt, Phys. Lett. B459, 570 (1999); P. Brax, J. Martin and A. Riazuelo, Phys. Rev. D62, 103505 (2000); R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); L. Wang and P. J. Steinhardt, Astrophys. J. 508, 483 (1998); R. R. Caldwell and P. J. Steinhardt, Phys. Rev. D57, 6057 (1998); P. F. González-Díaz, ibid. D62, 023513 (2000).
28. M. Melchiorri, L. Mersini, C. J. Odman and M. Tradden, astro-ph/0211522; M. Doupis, A. Riazuelo, Y. Zolnierowski and A. Blanchard, astro-ph/0212097; R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, astro-ph/0302506; G. W. Gibbons, hep-th/0302199; R. R. Caldwell, astro-ph/9908168.
29. M. Melchiorri, L. Mersini, C. J. Odman and M. Tradden, astro-ph/0211522; M. Doupis, A. Riazuelo, Y. Zolnierowski and A. Blanchard, astro-ph/0212097; R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, astro-ph/0302506; G. W. Gibbons, hep-th/0302199; R. R. Caldwell, astro-ph/9908168.
30. M. Melchiorri, L. Mersini, C. J. Odman and M. Tradden, astro-ph/0211522; M. Doupis, A. Riazuelo, Y. Zolnierowski and A. Blanchard, astro-ph/0212097; R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, astro-ph/0302506; G. W. Gibbons, hep-th/0302199; R. R. Caldwell, astro-ph/9908168.
31. M. Melchiorri, L. Mersini, C. J. Odman and M. Tradden, astro-ph/0211522; M. Doupis, A. Riazuelo, Y. Zolnierowski and A. Blanchard, astro-ph/0212097; R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, astro-ph/0302506; G. W. Gibbons, hep-th/0302199; R. R. Caldwell, astro-ph/9908168.
32. M. Melchiorri, L. Mersini, C. J. Odman and M. Tradden, astro-ph/0211522; M. Doupis, A. Riazuelo, Y. Zolnierowski and A. Blanchard, astro-ph/0212097; R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, astro-ph/0302506; G. W. Gibbons, hep-th/0302199; R. R. Caldwell, astro-ph/9908168.
33. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
34. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
35. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
36. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
37. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
38. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
39. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
40. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
41. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
42. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
43. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
44. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
45. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
46. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
47. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
48. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
49. P. J. E. Peebles and A. Vilenkin, Phys. Rev. D59, 063505 (1999); C. Baccigalupi and F. Perrota, astro-ph/981138385; M. Giovannini, Class. Quantum Grav. 16, 2905 (1999); Phys. Rev. D60, 123511 (1999); A. A. Sen, I. Chakrabarty and T. R. Seshadri, Gen. Rel. Grav. 34, 477 (2002); M. Peloso and F. Rosati, JHEP 12, 026 (1999); A. B. Kaganovich, Phys. Rev. D63, 025022 (2001); W. H. Kinney and A. Riotto, APP 10, 387 (1999); E. J. Copeland, A. R. Liddle and J. E. Lidsey, Phys. Rev. D64, 023509 (2001); K. Dimopoulos, Nucl. Phys. (Proc. Suppl.) 95, 70 (2001); G. Huey and J. Lidsey, Phys. Lett. B514, 217 (2001); A. S. Majumdar, Phys. Rev. D64, 083503 (2001); V. Sahni, M. Sami and T. Souradeep, ibid. D65, 023518 (2002); K. Dimopoulos and J. W. F. Valle, Astropart. Phys. 18, 287 (2002); M. Yahiro, G. J. Mathews, K. Ichiki, T. Kajino and M. Orito, Phys. Rev. D65, 063502 (2002); N. J. Nunes and E. J. Copeland, ibid. D66, 043524 (2002); K. Dimopoulos, astro-ph/0111500; astro-ph/0212264; astro-ph/0210374.
50. A. H. Campos, H. C. Reis and R. Rosenfeld, astro-ph/0210152.
51. J. J. Halliwell and R. Laflamme, Class. Quantum Grav. 6, 1839 (1989).
52. E. M. Lifshitz, J. Phys. 10, 116 (1946); E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963).
53. E. M. Lifshitz, J. Phys. 10, 116 (1946); E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12, 185 (1963).
54. W. Fischler, A. Kashani-Poor, R. McNees and S. Paban, JHEP 07, 003 (2001); S. Hellerman, N. Kaloper and L. Susskind, ibid. 06, 003 (2001); L. Dyson, M. Kleban and L. Susskind, ibid. 10, 011 (2002).
55. W. Fischler, A. Kashani-Poor, R. McNees and S. Paban, JHEP 07, 003 (2001); S. Hellerman, N. Kaloper and L. Susskind, ibid. 06, 003 (2001); L. Dyson, M. Kleban and L. Susskind, ibid. 10, 011 (2002).
56. W. Fischler, A. Kashani-Poor, R. McNees and S. Paban, JHEP 07, 003 (2001); S. Hellerman, N. Kaloper and L. Susskind, ibid. 06, 003 (2001); L. Dyson, M. Kleban and L. Susskind, ibid. 10, 011 (2002).
57. P. F. González-Díaz, Phys. Lett. B522, 211 (2001); Phys. Rev. D65, 104035 (2002).
58. P. F. González-Díaz, Phys. Lett. B522, 211 (2001); Phys. Rev. D65, 104035 (2002).s