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Exponential Potentials and Attractor Solution of Dilatonic Cosmology

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Abstract

We present the scalar-tensor gravitational theory with an exponential potential in which Pauli metric is regarded as the physical space-time metric. We show that it is essentially equivalent to coupled quintessence (CQ) model. However for baryotropic fluid being radiation there are in fact no coupling between dilatonic scalar field and radiation. We present the critical points for baryotropic fluid and investigate the properties of critical points when the baryotropic matter is specified to ordinary matter. It is possible for all the critical points to be attractors as long as the parameters λ and β satisfy certain conditions. To demonstrate the attractor behaviors of these critical points, We numerically plot the phase plane for each critical point. Finally with the bound on β from the observation and the fact that our universe is undergoing an accelerating expansion, we conclude that present accelerating expansion is not the eventual stage of universe. Moreover, we numerically describe the evolution of the density parameters Ω and the decelerating factor q, and computer the present values of some cosmological parameters, which are consistent with current observational data.

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References

  1. Spergel, D.N., et al.: astro-ph/0603449

  2. Steinhardt, P.J., Wang, L., Zlatev, I.: Phys. Rev. D 59, 123504 (1999)

    Article  ADS  Google Scholar 

  3. Steinhardt, P.: In: Fitch, V.L., Marlow, D.R. (eds.) Critical Problems in Physics. Princeton University Press, Princeton (1997)

    Google Scholar 

  4. Wetterich, C.: Nucl. Phys. B 302, 668 (1988)

    Article  ADS  Google Scholar 

  5. Ratra, B., Peebles, P.J.E.: Phys. Rev. D 37, 3406 (1988)

    Article  ADS  Google Scholar 

  6. Caldwell, R.R., Dave, R., Steinhardt, P.J.: Phys. Rev. Lett. 80, 1582 (1998)

    Article  ADS  Google Scholar 

  7. Steinhardt, P.J., Wang, L., Zlatev, I.: Phys. Rev. Lett. 82, 896 (1996)

    Google Scholar 

  8. Li, X.Z., Hao, J.G., Liu, D.J.: Class. Quantum Gravity 19, 6049 (2002)

    Article  MATH  ADS  Google Scholar 

  9. Armendáriz-Picón, C., Mukhanov, V., Steinhardt, P.J.: Phys. Rev. Lett. 85, 4438 (2000)

    Article  ADS  Google Scholar 

  10. Armendáriz-Picón, C., Mukhanov, V., Steinhardt, P.J.: Phys. Rev. D 63, 103510 (2001)

    Article  ADS  Google Scholar 

  11. Chiba, T.: Phys. Rev. D 66, 063514 (2002)

    Article  ADS  Google Scholar 

  12. Chiba, T., Okabe, T., Yamaguchi, M.: Phys. Rev. D 62, 023511 (2000)

    Article  ADS  Google Scholar 

  13. Malquarti, M., Copeland, E.J., Liddle, A.R., Trodden, M.: Phys. Rev. D 67, 123503 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  14. Sherrer, R.J.: Phys. Rev. Lett. 93, 011301 (2004)

    Article  ADS  Google Scholar 

  15. Chimento, L.P.: Phys. Rev. D 69, 123517 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  16. Melchiorri, A., Mersini, L., Odman, C.J., Trodden, M.: Phys. Rev. D 68, 043509 (2003)

    Article  ADS  Google Scholar 

  17. Feng, B., Li, M.Z., Piao, Y.S., Zhang, X.M.: Phys. Lett. B 634, 101–105 (2006)

    Article  ADS  Google Scholar 

  18. Guo, Z.K., Piao, Y.S., Zhang, X.M., Zhang, Y.Z.: Phys. Lett. B 608, 177–182 (2005)

    Article  ADS  Google Scholar 

  19. Xia, J.Q., Feng, B., Zhang, X.M.: Mod. Phys. Lett. A 20, 2409 (2005)

    Article  ADS  Google Scholar 

  20. Wei, H., Cai, R.G., Zeng, D.F.: Class. Quantum Gravity 22, 3189–3202 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. Zhao, G.B., Xia, J.Q., Li, M.Z., Feng, B., Zhang, X.M.: Phys. Rev. D 72, 123515 (2005)

    Article  ADS  Google Scholar 

  22. Wu, P.X., Yu, H.W.: Int. J. Mod. Phys. D 14, 1873–1882 (2005)

    Article  MATH  ADS  Google Scholar 

  23. Lazkoz, R., Len, G.: astro-ph/0602590

  24. Huang, Q.G., Li, M.: J. Cosmol. Astropart. Phys. 0408, 013 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  25. Ito, M.: Europhys. Lett. 71, 712–715 (2005)

    Article  ADS  Google Scholar 

  26. Ke, K., Li, M.: Phys. Lett. B 606, 173–176 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  27. Huang, Q.G., Li, M.: J. Cosmol. Astropart. Phys. 0503, 001 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  28. Gong, Y.G., Wang, B., Zhang, Y.Z.: Phys. Rev. D 72, 043510 (2005)

    Article  ADS  Google Scholar 

  29. Zhang, X.: Int. J. Mod. Phys. D 14, 1597–1606 (2005)

    Article  MATH  ADS  Google Scholar 

  30. Abramo, L.R., Finelli, F., Pereira, T.S.: Phys. Rev. D 70, 063517 (2004)

    Article  ADS  Google Scholar 

  31. Lu, H.Q.: Int. J. Mod. Phys. D 14, 355–362 (2005)

    Article  MATH  ADS  Google Scholar 

  32. Garousi, M.R., Sami, M., Tsujikawa, S.: Phys. Rev. D 71, 083005 (2005)

    Article  ADS  Google Scholar 

  33. Novello, M., Makler, M., Werneck, L.S., Romero, C.A.: Phys. Rev. D 71, 043515 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  34. Lu, H.Q., Huang, Z.G., Fang, W., Ji, P.Y.: hep-th/0504038

  35. Fuzfa, A., Alimi, J.M.: Phys. Rev. D 73, 023520 (2006)

    Article  ADS  Google Scholar 

  36. Fang, W., Lu, H.Q., Li, B., Zhang, K.F.: Int. J. Mod. Phys. D 15, 1947 (2006), hep-th/0512120

    Article  MATH  ADS  Google Scholar 

  37. Fang, W., Lu, H.Q., Huang, Z.G., Zhang, K.F.: Int. J. Mod. Phys. D 15, 199 (2006), hep-th/0409080

    Article  MATH  ADS  Google Scholar 

  38. Caldwell, R.R.: Phys. Lett. B 545, 23 (2002)

    Article  ADS  Google Scholar 

  39. Melchiorri, A.: astro-ph/0406652

  40. Faraoni, V.: Int. J. Mod. Phys. D 11, 471 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  41. Nojiri, S., Odintsov, S.D.: hep-th/0304131

  42. Nojiri, S., Odintsov, S.D.: hep-th/0306212

  43. Schulz, E., White, M.: Phys. Rev. D 64, 043514 (2001)

    Article  ADS  Google Scholar 

  44. Stachowiak, T., Szydllowski: hep-th/0307128

  45. Gibbons, G.W.: hep-th/0302199

  46. Feinstein, A., Jhingan, S.: hep-th/0304069

  47. Sami, M., Toporensky, A.: Mod. Phys. Lett. A 19, 1509 (2004)

    Article  ADS  Google Scholar 

  48. Lue, A., Scoccimarro, R., Starkman, G.: Phys. Rev. D 69, 044005 (2004)

    Article  ADS  Google Scholar 

  49. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  50. Meng, X.H., Wang, P.: Phys. Lett. B 584, 1–7 (2004)

    Article  ADS  Google Scholar 

  51. Nojiri, S., Odintsov, S.D.: Mod. Phys. Lett. A 19, 627–638 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  52. Carroll, S.M., et al.: Phys. Rev. D 71, 063513 (2005)

    Article  ADS  Google Scholar 

  53. Faraoni, V.: Phys. Rev. D 72, 061501 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  54. Koyama, K.: J. Cosmol. Astropart. Phys. 0603, 017 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  55. Gumjudpai, B., Naskar, T., Sami, M., Tsujikawa, S.: hep-th/0502191

  56. Copeland, E.J., Sami, M., Tsujikawa, S.: hep-th/0603057

  57. Bean, R., Magueijo, J.: Phys. Lett. B 517, 177–183 (2001)

    Article  MATH  ADS  Google Scholar 

  58. Damour, T., Piazza, F., Veneziano, G.: Phys. Rev. Lett. 89, 081601 (2002)

    Article  ADS  Google Scholar 

  59. Susperregi, M.: Phys. Rev. D 68, 123509 (2003)

    Article  ADS  Google Scholar 

  60. Piazza, F., Tsujikawa, S.: J. Cosmol. Astropart. Phys. 0407, 004 (2004)

    Article  ADS  Google Scholar 

  61. Boisseau, B., Esposito-Farese, G., Polarski, D., Starobinsky, A.A.: Phys. Rev. Lett. 85, 2236 (2000)

    Article  ADS  Google Scholar 

  62. Esposito-Farese, G., Polarski, D.: Phys. Rev. D 63, 063504 (2001)

    Article  ADS  Google Scholar 

  63. Huang, Z.G., Lu, H.Q.: Int. J. Mod. Phys. D 15, 1501 (2006)

    Article  MATH  ADS  Google Scholar 

  64. Lu, H.Q., Huang, Z.G., Fang, W.: hep-th/0409309

  65. Lu, H.Q., Cheng, K.S.: Astrophys. Space Sci. 235, 207 (1996)

    Article  MATH  ADS  Google Scholar 

  66. Gong, Y.G.: gr-qc/9809015

  67. Huang, Z.G., Lu, H.Q., Fang, W.: Class. Quantum Gravity 23, 6215 (2006), hep-th/0604160

    Article  MATH  MathSciNet  Google Scholar 

  68. Copeland, E.J., Liddle, A.R., Wands, D.: Phys. Rev. D 57, 4686 (1998)

    Article  ADS  Google Scholar 

  69. Gong, Y.G., et al.: Phys. Lett. B 636, 286–292 (2006)

    ADS  MathSciNet  Google Scholar 

  70. Halliwell, J.J.: Phys. Lett. B 185, 341 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  71. Burd, A.B., Barrow, J.D.: Nucl. Phys. B 308, 929 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  72. Coley, A.A., Ibanez, J., van den Hoogen, R.J.: J. Math. Phys. 38, 5256 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  73. Finelli, F., Brandenberger, R.: Phys. Rev. D 65, 103522 (2002)

    Article  ADS  Google Scholar 

  74. Heard, I.P.C., Wands, D.: Class. Quantum Gravity 19, 5435–5448 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  75. Elizalde, E., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 70, 043539 (2004)

    Article  ADS  Google Scholar 

  76. Nunes, N.J., Mota, D.F.: Mon. Not. Roy. Astron. Soc. 368, 751–758 (2006)

    Article  ADS  Google Scholar 

  77. Hartong, J., Ploegh, A., Riet, T.V., Westra, D.B.: gr-qc/0602077

  78. Wetterich, C.: Nucl. Phys. B 302, 668 (1988)

    Article  ADS  Google Scholar 

  79. Wands, D., Copeland, E.J., Liddle, A.R.: Ann. Acad. Sci. (N.Y.) 688, 647 (1993)

    Article  ADS  Google Scholar 

  80. Cho, Y.M.: Phys. Rev. Lett. 68, 3133 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  81. Damour, T., Nordtvedt, K.: Phys. Rev. D 48, 3436 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  82. Damour, T., Nordtvedt, K.: Phys. Rev. Lett. 70, 2217 (1993)

    Article  ADS  Google Scholar 

  83. Reasenberg, R.D., et al.: Astrophys. J. 234L, 219 (1979)

    Article  ADS  Google Scholar 

  84. Bertotti, B., Iess, L., Tortora, P.: Nature 425, 374 (2003)

    Article  ADS  Google Scholar 

  85. Amendola, L.: Phys. Rev. D 62, 043511 (2000)

    Article  ADS  Google Scholar 

  86. Amendola, L.: Phys. Rev. D 60, 043501 (1999)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Shanghai University, Shanghai, 200444, China

    Wei Fang & H. Q. Lu

  2. Department of Mathematics and Physics, Huaihai Institute of Technology, Lianyungang, 222005, China

    Z. G. Huang

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  1. Wei Fang
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  2. H. Q. Lu
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  3. Z. G. Huang
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Correspondence to Wei Fang.

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Fang, W., Lu, H.Q. & Huang, Z.G. Exponential Potentials and Attractor Solution of Dilatonic Cosmology. Int J Theor Phys 46, 2366–2377 (2007). https://doi.org/10.1007/s10773-007-9354-x

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