中高能物理与宇宙学中的热力学统计物理问题
|
摘要
热力学与统计物理是处理由大量客体构成的体系的宏观物理性质的重要理论工具,在物理世界中有着广泛而重要的应用。本论文主要讨论这一理论物理学的重要分支在中高能物理、广义相对论等诸多方面的相关应用。主要涉及以下问题：有效质量近似下准粒子体系的热力学自恰性、弱超子-超子相互作用下奇异强子物质的汽液相变、手征SU(3)夸克平均场模型中的慢转中子星与强子星的最大质量、有限温度效应在暴涨宇宙中对微波背景辐射谱的影响、高维德西特膜宇宙中嵌入黑洞的能量与熵的辐射、5维AdS时空中非平凡拓扑弯曲黑弦的稳定性等等。我们将看到温度、统计、熵等热力学与统计物理的核心概念在各个领域中的相关问题及重要应用。
本文主要解决了如下问题：
1.通过在热力学可逆过程的描述中引入有效质量作为新的独立变量,我们成功地解决了有效质量近似下准粒子体系的热力学自洽性问题。通过两个具体实例,汪实了我们的处理方案可以很好地描述高能物理学中各种不同的准粒子模型。相比于旧的处理方案,我们的结果与合理的理论预期或格点数据更为相符。此外,将有效质量作为独立变量后允许对压强和熵引入一个作为有效质量任意函数的修正,这一修正使得准粒子模型能够自然且自洽地实现期望的负压强。
2.根据新近实验发现的弱超子相互作用结果,我们重新研究了奇异强子物质的汽液相变,发现弱的超子相互作用将使得体系的稳定性降低,汽液相变更易于发生。
3.为考察致密星体的最大质量上限,我们考虑了慢转效应对星体结构的修正。我们发现,转动可以有效地提升星体的最大质量,但在手征SU(3)夸克平均场模型下,奇异强子物质的状态方程过软,由其构成的奇异强子星不足以解释天文观测发现的超重脉冲星的质量。
4.我们通过考虑有限温度的效应,将暴涨场原初扰动的真空取为热真空,利用热场动力学方法得到了能谱的有限温度修正。对微波背景辐射谱的拟合显示,考虑了有限温度修正后的能谱能够更好地解释天文观测结果。
5.对于高维德西特时空中的黑洞,通过全面讨论其能量与熵的各种模式的辐射,我们发现辐射过程中黑洞损失的熵与辐射得到的熵在数值上总是基本相当的,这一结果倾向于支持贝肯斯坦对于黑洞熵的猜想。
6.通过研究5维反德西特空间中扭曲黑弦的张量引力扰动,我们发现不同拓扑与不同半径的黑弦都存在不稳定性,这种不稳定性的出现取决于扰动在第五维空间中的模式。这一不稳定性条件对联系动力学不稳定性与热力学不稳定性的理论尝试提出了新的挑战。
7.作为附带介绍关于额外维空间在宇宙学中的相关问题,我们还研究了带有额外维物质的Dvali-Gabadadze-Porrati膜宇宙中等效暗能量状态方程的转变。数值结果显示,额外维物质的引入使得有效暗能量状态方程能够发生转变,其中额外维物质的存在,而不是额外维与膜宇宙之间的能流,对于膜上宇宙的状态方程转变有至关重要的作用。
Thermodynamics and statistical physics are very important theoretical tools in studying the macroscopic properties of system consisting of many objects. This thesis is devoted to the related application of this important branch of the theoretical physics in the fields of the high energy physics and general relativity, such as, the thermodynamic consistency of quasiparticle system with effective mass, the liquid-gas phase transition of strange hadronic matter with weak hyperon-hyperon interaction, slowly rotating neu-tron stars and hadronic stars in the chiral SU(3) quark mean field model, temperature effect on the power spectrum in inflation, energy and entropy radiated by a black hole embedded in a higher dimensional de Sitter braneworld, stability of warped black string with nontrivial topology in 5 dimensional Anti-de Sitter spacetime, etc. We will see that the important thermodynamic concepts, such as temperature, statistics, entropy, have very important applications in many fields of physics.
The main conclusions of this thesis are as follows:
1. By introducing the effective mass as a new independent variable in the description of the thermodynamic reversible process, we have successfully solved the thermo-dynamic consistency problem of quasiparticle system with effective mass. Via two concrete models as examples, our treatment is applicable to different quasiparticle systems. Compared with the old treatments, our results are more consistent with theoretical predictions or lattice data. Besides, the introduction of effective mass as a new independent variable makes it possible to modify the pressure and en-tropy by an arbitrary function of the effective mass, which results in the expected instability of negative pressure naturally and self-consistently.
2. With the result of weak Y-Y interaction reported in the recent experiment, we reexamined the liquid-gas phase transition of the strange hadronic matter, and find that, with the weak interaction, the system becomes more unstable and the phase transition can happen more easily.
3. In order to examine the upper limit of the maximum mass of compact stars, we consider the correction to the stellar structure from slow rotation. We find the rotation can increase the maximum mass significantly, but the maximum mass of the strange hadronic star in the chiral SU(3) quark mean-field model is still too small to explain the massive pulsar observed, because the equation of state of the strange hadronic matter is too soft.
4. By taking the thermal vacuum of the inflaton field to include the finite temper-ature effect, we obtain the finite temperature correction to the spectrum by the thermal field dynamics. After fitting with the cosmic microwave background radi-ation spectrum, we find that the modified spectrum can explain the observational data better.
5. After completely examine the different modes of the radiation of energy and entropy of the black hole in higher dimensional de-Sitter spacetime, we find the entropy lost by the black hole and obtained in the radiation are always of the same order in the radiation process, which is in favor of the Bekenstein's conjecture about black hole entropy.
6. By the study of the gravitational tensor perturbation of the warped black string in 5 dimensional anti-de-Sitter spacetime, we find that the instability exists in different topologies and radii, depending on the mode of the perturbation in the 5th dimension. This condition for instability challenges the relation between the dynamic instability and thermodynamic instability.
7. Besides, we also studied the transition of effective equation of state of dark energy in the Dvali-Gabadadze-Porrati braneworld model with bulk content. Our numerical results show that the introduction of bulk content can realize the transition of the effective equation of state of dark energy within this model, where the bulk matter, rather than the energy flow between the bulk and brane, plays the key role.
本文主要解决了如下问题：
1.通过在热力学可逆过程的描述中引入有效质量作为新的独立变量,我们成功地解决了有效质量近似下准粒子体系的热力学自洽性问题。通过两个具体实例,汪实了我们的处理方案可以很好地描述高能物理学中各种不同的准粒子模型。相比于旧的处理方案,我们的结果与合理的理论预期或格点数据更为相符。此外,将有效质量作为独立变量后允许对压强和熵引入一个作为有效质量任意函数的修正,这一修正使得准粒子模型能够自然且自洽地实现期望的负压强。
2.根据新近实验发现的弱超子相互作用结果,我们重新研究了奇异强子物质的汽液相变,发现弱的超子相互作用将使得体系的稳定性降低,汽液相变更易于发生。
3.为考察致密星体的最大质量上限,我们考虑了慢转效应对星体结构的修正。我们发现,转动可以有效地提升星体的最大质量,但在手征SU(3)夸克平均场模型下,奇异强子物质的状态方程过软,由其构成的奇异强子星不足以解释天文观测发现的超重脉冲星的质量。
4.我们通过考虑有限温度的效应,将暴涨场原初扰动的真空取为热真空,利用热场动力学方法得到了能谱的有限温度修正。对微波背景辐射谱的拟合显示,考虑了有限温度修正后的能谱能够更好地解释天文观测结果。
5.对于高维德西特时空中的黑洞,通过全面讨论其能量与熵的各种模式的辐射,我们发现辐射过程中黑洞损失的熵与辐射得到的熵在数值上总是基本相当的,这一结果倾向于支持贝肯斯坦对于黑洞熵的猜想。
6.通过研究5维反德西特空间中扭曲黑弦的张量引力扰动,我们发现不同拓扑与不同半径的黑弦都存在不稳定性,这种不稳定性的出现取决于扰动在第五维空间中的模式。这一不稳定性条件对联系动力学不稳定性与热力学不稳定性的理论尝试提出了新的挑战。
7.作为附带介绍关于额外维空间在宇宙学中的相关问题,我们还研究了带有额外维物质的Dvali-Gabadadze-Porrati膜宇宙中等效暗能量状态方程的转变。数值结果显示,额外维物质的引入使得有效暗能量状态方程能够发生转变,其中额外维物质的存在,而不是额外维与膜宇宙之间的能流,对于膜上宇宙的状态方程转变有至关重要的作用。
Thermodynamics and statistical physics are very important theoretical tools in studying the macroscopic properties of system consisting of many objects. This thesis is devoted to the related application of this important branch of the theoretical physics in the fields of the high energy physics and general relativity, such as, the thermodynamic consistency of quasiparticle system with effective mass, the liquid-gas phase transition of strange hadronic matter with weak hyperon-hyperon interaction, slowly rotating neu-tron stars and hadronic stars in the chiral SU(3) quark mean field model, temperature effect on the power spectrum in inflation, energy and entropy radiated by a black hole embedded in a higher dimensional de Sitter braneworld, stability of warped black string with nontrivial topology in 5 dimensional Anti-de Sitter spacetime, etc. We will see that the important thermodynamic concepts, such as temperature, statistics, entropy, have very important applications in many fields of physics.
The main conclusions of this thesis are as follows:
1. By introducing the effective mass as a new independent variable in the description of the thermodynamic reversible process, we have successfully solved the thermo-dynamic consistency problem of quasiparticle system with effective mass. Via two concrete models as examples, our treatment is applicable to different quasiparticle systems. Compared with the old treatments, our results are more consistent with theoretical predictions or lattice data. Besides, the introduction of effective mass as a new independent variable makes it possible to modify the pressure and en-tropy by an arbitrary function of the effective mass, which results in the expected instability of negative pressure naturally and self-consistently.
2. With the result of weak Y-Y interaction reported in the recent experiment, we reexamined the liquid-gas phase transition of the strange hadronic matter, and find that, with the weak interaction, the system becomes more unstable and the phase transition can happen more easily.
3. In order to examine the upper limit of the maximum mass of compact stars, we consider the correction to the stellar structure from slow rotation. We find the rotation can increase the maximum mass significantly, but the maximum mass of the strange hadronic star in the chiral SU(3) quark mean-field model is still too small to explain the massive pulsar observed, because the equation of state of the strange hadronic matter is too soft.
4. By taking the thermal vacuum of the inflaton field to include the finite temper-ature effect, we obtain the finite temperature correction to the spectrum by the thermal field dynamics. After fitting with the cosmic microwave background radi-ation spectrum, we find that the modified spectrum can explain the observational data better.
5. After completely examine the different modes of the radiation of energy and entropy of the black hole in higher dimensional de-Sitter spacetime, we find the entropy lost by the black hole and obtained in the radiation are always of the same order in the radiation process, which is in favor of the Bekenstein's conjecture about black hole entropy.
6. By the study of the gravitational tensor perturbation of the warped black string in 5 dimensional anti-de-Sitter spacetime, we find that the instability exists in different topologies and radii, depending on the mode of the perturbation in the 5th dimension. This condition for instability challenges the relation between the dynamic instability and thermodynamic instability.
7. Besides, we also studied the transition of effective equation of state of dark energy in the Dvali-Gabadadze-Porrati braneworld model with bulk content. Our numerical results show that the introduction of bulk content can realize the transition of the effective equation of state of dark energy within this model, where the bulk matter, rather than the energy flow between the bulk and brane, plays the key role.
引文
[1]B. D. Serot and J. D. Walecka, Inter. Jour. Mod. Phys. E 6,515 (1997) and references therein.
[2]G. E. Brown and M. Rho, Phys. Rev. Lett 66,2720 (1991).
[3]K. Saito, K. Tsushima and A. W. Thomas, Phys. Rev. C 56,566 (1997).
[4]G. J. Lolos et. al., Phys. Rev. Lett.80,241 (1998).
[5]G. N. Fowler, S. Raha and R. M. Weiner, Z. Phys. C 9,271 (1981).
[6]V. Goloviznin and H. Satz, Z. Phys. C 57,671 (1993).
[7]A. Peshier, B. Kampfer,0. P. Pavlenko, and G. Soff, Phys. Lett. B337,235 (1994).
[8]M. I. Gorenstein and S. N. Yang, Phys. Rev. D 52,5206 (1995).
[9]M. Bluhm, B. Kampfer, and G. Soff, Phys. Lett. B620,131 (2005).
[10]V. M. Bannur, Phys. Lett. B647,271 (2007); Phys. Rev. C 75,044905 (2007).
[11]S. Chakrabarty, S. Raha, and B. Sinha, Phys. Lett. B229,112 (1989).
[12]S. Chakrabarty, Phys. Rev. D 43,627 (1991).
[13]S. Chakrabarty, Phys. Rev. D 48,1409 (1993).
[14]O. G. Benvenuto and G. Lugones, Phys. Rev. D 51,1989 (1995).
[15]G. Lugones and O. G. Benvenuto, Phys. Rev. D 52,1276 (1995).
[16]G. X. Peng, H. C. Chiang, P. Z. Ning, and B. S. Zou, Phys. Rev. C 59,3452 (1999).
[17]G. X. Peng et al., Phys. Rev. C 62,025801 (2000).
[18]P. Wang, Phys. Rev. C 62,015204 (2000).
[19]Y. Zhang, R. K. Su, S. Q. Ying, and P. Wang, Euro. Phys. Lett.56,361 (2001).
[20]Y. Zhang and R. K. Su, Phys. Rev. C 65,035202 (2002).
[21]Y. Zhang and R. K. Su, Phys. Rev. C 67,015202 (2003).
[22]X. J. Wen et al., Phys. Rev. C 72,015204 (2005).
[23]C. Wu, W. L. Qian and R. K. Su, Phys. Rev. C 72,035205 (2005); Chin. Phys. Lett.22,1866 (2005).
[24]H. Mao, R. K. Su, and W. Q. Zhao, Phys. Rev. C 74,055204 (2006).
[25]S. Yin and R. K. Su, Phys. Rev. C 77,055204 (2008).
[26]S. Yin and R. K. Su, Int. J. Mod. Phys. A,25,1449 (2010).
[27]A. Das, Finite Temperature Field Theory (World Scientific, Singapore,1997).
[28]J. P. Blaizot, E. Iancu, and A. Rebhan, Phys. Rev. D 63,065003 (2001).
[29]Y. J. Zhang, S. Gao, and R. K. Su, Phys. Rev. C 56,3336 (1997).
[30]H. Shiomi and T. Hatsuda, Phys. Lett. B334,281 (1994).
[31]V. K. Gupta, A. Gupta, S. Singh, and J. D. Anand, Int. J. Mod. Phys. D 12,583 (2003).
[32]J. Y. Shen, Y. Zhang, B. Wang, and R. K. Su, Int. J. Mod. Phys. A 20,7547 (2005).
[33]E. Farhi and R. L. Jaffe, Phys. Rev, D 30,2379 (1984).
[34]J. Adams et al. [STAR Collaboration], Nucl. Phys. A757,102 (2005).
[35]K. Adcox et al. [PHENIX Collaboration], Nucl. Phys. A757,184 (2005).
[36]T. S. Biro, A. A. Shanenko, and V. D. Toneev, Phys. Atom. Nucl.66,982 (2003).
[37]J. Engels et al., Z. Phys. C 42,341 (1989).
[38]G. Boyd et al., Phys. Rev. Lett.75,4169 (1995); Nucl. Phys. B469,419 (1996).
[39]J. Schaffner, C. Greiner,and H. Stoecker, Phys. Rev. C 46,322 (1992).
[40]C. Greiner and J. Schaffner-Bielich, "Physics of strange matter", "Heavy Elements and Related New Phenomena", Vol Ⅱ, p1074, by R. K. Gupta and W. Greiner, World Scientific Publications (1999). [arXiv:nucl-th/9801062]
[41]N. K. Glendenning, Phys. Rev. C 23,2757 (1981).
[42]P. Papazoglou et al., Phys. Rev. C 57,2576 (1998).
[43]P. Papazoglou et al., Phys. Rev. C 59,411 (1999).
[44]J. Schaffner et al., Phys. Rev. Lett.71,1328 (1993).
[45]J. Schaffner et al., Annals Phys.235,35 (1994).
[46]J. Schaffner and A. Gal, Phys. Rev. C 62,034311 (2000).
[47]K. Saito and A. W. Thomas, Phys. Lett. B327,9 (1994).
[48]P. Wang, R. K. Su, H. Q. Song, and L. L. Zhang, Nucl. Phys. A653,166 (1999).
[49]R. J. Furnstahl, H. B. Tang, and B. D. Serot, Phys. Rev. C 52,1368 (1995); R. J. Furnstahl, B. D. Serot, and H. B. Tang, Nucl. Phys. A598,539 (1996); ibid. A615, 441 (1997).
[50]M. Danysz et al., Nucl. Phys.49,121 (1963).
[51]R. H. Dalitz et al., Proc. Rol. Soc. Ser. A 426,1 (1989).
[52]C. Beckmann et al., Phys. Rev. C 65,024301 (2002).
[53]L. Yang, W. L. Qian, R. K. Su, and H. Q. Song, Phys. Rev. C 70,045207 (2004).
[54]P. Wang, D. B. Leinweber, A. W. Thomas, and A. G. Williams, Phys. Rev. C 70, 055204 (2004).
[55]H. Takahashi et al, Phys. Rev. Lett.87,212502 (2001).
[56]D. J. Prowse, Phys. Rev. Lett.17,282 (1966).
[57]S. Aoki et al., Prog. Theor. Phys.85,1287 (1991).
[58]C. B. Dover, D. J. Millener, A. Gal, and D. H. Davis, Phys. Rev. C 44,1905 (1991).
[59]H. Q. Song, R. K. Su, D. H. Lu, and W. L. Qian, Phys. Rev. C 68,055201 (2003).
[60]W. L. Qian, R. K. Su, and H. Q. Song, J. Phys. G 30,1893 (2004).
[61]L. L. Zhang, H. Q. Song, P. Wang, and R. K. Su, J. Phys. G 26,1301 (2000).
[62]W. L. Qian, R. K. Su, and H. Q. Song, Commun. Theor. Phys.40,466 (2003).
[63]H. J. Schulze et al., Phys. Rev. C 57,704 (1998).
[64]Y. Zhang and R. K. Su, Mod. Phys. Lett. A 18,143 (2003).
[65]L. Yang, S. Yin, W. Qian, and R. K. Su, Phys. Rev. C 73,025203 (2006).
[66]H. Muller and B. D. Serot, Phys. Rev. C 52,2072 (1995).
[67]W. L. Qian, R. K. Su, and P. Wang, Phys. Lett. B491,90 (2000).
[68]W. L. Qian, R. K. Su, and H. Q. Song, Phys. Lett. B520,217 (2001).
[69]W. L. Qian, R. K. Su, and H. Q. Song, J. Phys. G 28,379 (2002).
[70]W. L. Qian and R. K. Su, J. Phys. G 29,1023 (2003).
[71]D. J. Millener, A. Gal, C. B. Dover, and R. H. Dalitz, Phys. Rev. C 31,499 (1985).
[72]V. M. Kolomietz, A. I. Sanzhur, S. Shlomo, and S. A. Firin, Phys. Rev. C 64,024315 (2001).
[73]L. G. Moretto et al., Phys. Rev. Lett.76,2822 (1996).
[74]Y. G. Ma et al., Phys. Rev. C 69,031604(R) (2004).
[75]Y. G. Ma et al., Phys. Rev. C 71,054606 (2005).
[76]T. Sil, S. K. Samaddar, J. N. De, and S. Shlomo, Phys. Rev. C 69,014602 (2004).
[77]A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins, Nature, 217,709 (1968).
[78]D. G. Ravenhall and C. J. Pethick, Astrophys. J.424,846 (1994).
[79]V. Kalogera and D. Psaltis, Phys. Rev. D 61,024009 (1999).
[80]M. Prakash et al., Phys. Rep.280,1 (1997).
[81]S. Gupta et al., Astrophys. J.662,1188 (1971).
[82]G. Baym, C. Pethick, and P. Sutherland, Astrophys. J.170,299 (1971).
[83]N. K. Glendenning, Astrophys. J.293,470 (1985).
[84]C. Wu and R. K. Su, J. Phys. G 36,095101 (2009).
[85]J. M. Lattimer and M. Prakash, Astrophys. J.550,426 (2001).
[86]T. Klahn et al., Phys. Rev. C 74,035802 (2006).
[87]J. M. Lattimer and M. Prakash, Phys. Rep.442,109 (2007).
[88]E. Witten, Phys. Rev. D 30,272 (1984).
[89]P. Haensel, J. L. Zdunik, and R. Schaefer, Astron. Astrophys.160,121 (1986).
[90]C. Alcock, E. Farhi, and A. Olinto, Astrophys. J.310,261 (1986).
[91]R. X. Xu, Astrophys. J.596, L59 (2003).
[92]F. Weber, Prog. Part. Nucl. Phys.54,193 (2005).
[93]V. A. Ambartsumyan and G. S. Saakyan, Soviet Astr.-AJ 4,187 (1960).
[94]N. K. Glendenning, Phys. Lett. B114,392 (1982).
[95]J. Schaffner and I. N. Mishustin, Phys. Rev. C 53,1416 (1996).
[96]M. Baldo, G. F. Burgio, and H.-J. Schulze, Phys. Rev. C 58,3688 (1998); ibid.61, 055801 (2000).
[97]P. Wang, Z. Y. Zhang, Y. W. Yu, R. K. Su, and H. Q. Song, Nucl. Phys. A688,791 (2001).
[98]P. Wang, H. Guo, Z. Y. Zhang, Y. W. Yu, R. K. Su, and H. Q. Song, Nucl. Phys. A705,455 (2002).
[99]P. Wang, S. Lawley, D. B. Leinweber, A. W. Thomas, and A. G. Williams, Phys. Rev. C 72,045801 (2005).
[100]P. C. C. Champion, arXiv:0907.3219.
[101]S. Yin, J. Zang and R. K. Su, Eur. Phys. J. A 43,295 (2010).
[102]J. B. Hartle, Astrophys. J.150,1005 (1967); J. B. Hartle and K. S. Thorne, Astrophys. J.153,807 (1968).
[103]T. Regge and J. A. Wheeler, Phys. Rev.108,1063 (1957).
[104]J. M. Lattimer and M. Prakash, Science,304,536 (2004).
[105]P. W. Anderson and N. Itoh, Nature 256,25 (1975).
[106]N. K. Glendenning and F. Weber, Astrophys. J.400,647 (1992).
[107]J. L. Zdunik, P. Haensel, and E. Gourgoulhon, Astron. Astrophys.,372,535 (2001).
[108]J. W. Negele and D. Vautherin, Nucl. Phys. A207,298 (1974).
[109]S. B. Ruster, M. Hempel, and J. Schaffner-Bielich, Phys. Rev. C 73,035804 (2006).
[110]F. Weber and N. K. Glendenning, Astrophys. J.390,541 (1992).
[111]M. Hanauske et al., Astrophys. J.537,958 (2000).
[112]S. Schramm and D. Zschiesche, J. Phys. G 29,531 (2003).
[113]G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Astrophys. J.398,203 (1992); ibid.422,227 (1994).
[114]T. W. Baumgarte, S. L. Shapiro, and M. Shibata, Astrophys. J.528, L29 (2000).
[115]N. D. Lyford, T. W. Baumgarte, and S. L. Shapiro, Astrophys. J.583,410 (2003).
[116]I. A. Morrison, T. W. Baumgarte, and S. L. Shapiro, Astrophys. J.610,941 (2004).
[117]G. F. Burgio, H.-J. Schulze, and F. Weber, Astron. Astrophys.408,675 (2003).
[118]Baldo et al., arxiv:astro-ph/0312446.
[119]N. K. Glendenning, Phys. Rev. D 46,1274 (1992).
[120]A. Rosenhauer et al., Nucl. Phys. A540,630 (1992).
[121]F. Weber, J. Phys. G 25, R195 (1999).
[122]M. Alford et al., Nature 455, E7 (2007).
[123]L. McLerran and R. D. Pisarski, Nucl. Phys. A796,83 (2007).
[124]L. Ya. Glozman and R. F. Wagenbrunn, Phys. Rev. D 77,054027 (2008).
[125]A. H. Guth, Phys. Rev. D 23,347 (1981).
[126]A. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur, Switzerland,1990), arXiv:hep-th/0503203.
[127]A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge,.England,2000).
[128]R. Easther, B. R. Greene, W. H. Kinney, and G. Shiu, Phys. Rev. D 64,103502 (2001).
[129]R. Easther, B. R. Greene, W. H. Kinney, and G. Shiu, Phys. Rev. D 66,023518 (2002).
[130]U. F. Danielsson, Phys. Rev. D 66,023511 (2002).
[131]B. Wang, L. H. Xue, Z. Zhang, and W-Y. P Hwang, Phys. Rev. D 67,123519 (2003).
[132]K. Goldstein and D. A. Lowe, Phys. Rev. D 67,063502 (2003).
[133]J. Martin and C. Ringeval, Phys. Rev. D 69,083515 (2004); ibid.127303 (2004).
[134]J. Martin and C. Ringeval, J. Cosmol. Astropart. Phys.01,007 (2005); ibid.08, 009 (2006).
[135]J. Ren, H.-G. Zhang, and X.-H. Meng, Int. J. Mod. Phys. D 18,1343 (2009).
[136]N. E. Groeneboom and (?)stein Elgar(?)y, Phys. Rev. D 77,043522 (2008).
[137]U. H. Danielsson, J. High Energy Phys.12,025 (2002).
[138]R. H. Brandenberger, hep-th/0210186.
[139]X. Wang, B. Feng, and M. Li, Int. J. Mod. Phys. D 14,1347 (2005).
[140]C. P. Burgess, J. M. Cline, F. Lemieux, and R. Holman, J. High Energy Phys.02, 048 (2003).
[141]N. A. Chernikov and E. A. Tagirov, Ann. Inst. Henri Poincare, vol. Ⅸ,2,109 (1968).
[142]E. Mottola, Phys. Rev. D 31,754 (1985).
[143]B. Allen, Phys. Rev. D 32,3136 (1985).
[144]R. Floreanini, C. T. Hill, and R. Jackiw, Ann. Phys. (NY) 175,345 (1987).
[145]R. Bousso, A. Maloney, and A. Strominger, Phys. Rev. D 65,104039 (2002).
[146]M. Spradlin and A. Volovich, Phys. Rev. D 65,104037 (2002).
[147]A. H. Guth and S.-Y. Pi, Phys. Rev. D 32,1899 (1985).
[148]K. Bhattacharya, S. Mohanty, and R. Rangarajan, Phys. Rev. Lett.96,121302 (2006); ibid.97,231301 (2006).
[149]S. Yin, B. Wang, R. K. Su, Phys. Lett. B675,84 (2009).
[150]H. Umezawa, H. Matsumoto, and M. Tachiki. Thermo field dynamics and condensed states (North-Holland, Amsterdam,1982).
[151]L. Bergstrom and U. F. Danielsson, J. High Eenergy Phys.12,038 (2002).
[152]G. Hinshaw et al., Astrophys. J. Suppl.180,225 (2009).
[153]K. Enqvist, M. S. Sloth, Phys. Rev. Lett.93,221302 (2004); K. Enqvist, S. Hannes-tad, and M. S. Sloth, JCAP 02,004 (2005).
[154]J. Shen, B. Wang, E. Abdalla, and R.-K. Su, Phys. Lett. B609,200 (2005).
[155]A. G. Cohen, A.B. Kaplan, and A. E. Nelson, Phys. Rev. Lett 82,4971 (1999).
[156]M. Giovanini, Int. J. Mod. Phys. D 14,363 (2005).
[157]T. Banks and W. Fischler, hep-th/9906038.
[158]S. Dimopoulos and G. Landsberg, Phys. Rev. Lett.87,161602 (2001).
[159]S. B. Giddings and S. Thomas, Phys. Rev. D 65,056010 (2002).
[160]V. Cardoso, J. P. S. Lemos, and S. Yoshida, Phys. Rev. D 69,044004 (2004).
[161]D. Stojkovic, Phys. Rev. Lett.94,011603 (2005).
[162]R. d. Rocha, C. H. Coimbra-Araujo, Phys. Rev. D 74,055006 (2006).
[163]M. Cavaglia, R. Godang, L. M. Cremaldi, D. J. Summers, J. High Energy Phys. 06,055 (2007).
[164]A. Goyal, A. Gupta, and N. Mahajan, Phys. Rev. D 63,043003 (2001).
[165]J. L. Feng and A. D. Shapere, Phys. Rev. Lett.88,021303 (2002).
[166]E. J. Ahn, M. Ave, M. Cavaglia, and A.V. Olinto, Phys. Rev. D 68,043004 (2003).
[167]T. Han and D. Hooper, New J. Phys.6,150 (2004).
[168]A. Cafarella, C. Coriano, and T. N. Tomaras, J. High Energy Phys.06,065 (2005).
[169]D. Stojkovic and G. D. Starkman, Phys. Rev. Lett.96,041303 (2006).
[170]L. A. Anchordoqui, M. M. Glenz, and L. Parker, Phys. Rev. D 75,024011 (2007).
[171]P. Kanti, Int. J. Mod. Phys. A 19,4899 (2004).
[172]A. Barrau, J. Grain, and S. O. Alexeyev, Phys. Lett. B584,114 (2004).
[173]J. Grain, A. Barrau, and P. Kanti, Phys. Rev. D 72,104016 (2005).
[174]P. Kanti, J. Grain and A. Barrau, Phys. Rev. D 71,104002 (2005).
[175]J. Maldacena, Adv. Theor. Math. Phys.2,231 (1998).
[176]S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B428,105 (1998).
[177]E. Witten, Adv. Theor. Math. Phys.2,253 (1998).
[178]A. G. Riess et al., Astrophys. J.659,98 (2007).
[179]G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15,2738 (1977).
[180]R. L. Mallett, Phys. Rev. D 3,2201 (1986).
[181]P. C. W. Davies, L. H. Ford, and D. N. Page, Phys. Rev. D 34,1700 (1986).
[182]W. H. Huang, Class. Quant. Grav.9,1199 (1992).
[183]R. Bousso and S. W. Hawking, Phys. Rev. D 57,2436 (1998).
[184]O. J. C. Dias and J. P. S. Lemos, Phys. Rev. D 70,124023 (2004).
[185]A. J. M. Medved, Phys. Rev. D 66,124009 (2002).
[186]V. Balasubramanian, J. de Boer, and D. Minic, Phys. Rev. D 65,123508 (2002).
[187]R. G. Cai, Y. S. Myung, and Y. Z. Zhang, Phys. Rev. D 65,084019 (2002).
[188]A. M. Ghezelbach and R. B. Mann, J. High Energy Phys.01,005 (2002).
[189]C. Molina, Phys. Rev. D 68,064007 (2003).
[190]V. Cardoso, O. J. C. Dias and J. P. S. Lemos, Phys. Rev. D 70,024002 (2004).
[191]J. Natario and R. Schiappa, Adv. Theor. Math. Phys.8,1001 (2004).
[192]J. Labbe, A. Barrau, and J. Grain, Proc. Sci., HEP2005,013 (2006) [arXiv:hep-ph/0511211].
[193]T. Harmark, J. Natario, and R. Schiappa, arXiv:0708.0017.
[194]S. F. Wu, S. Yin, G. H. Yang, and P. M. Zhang, Phys. Rev. D 78,084010 (2008).
[195]J.D. Bekenstein, Phys. Rev. D 7,2333 (1973).
[196]A. Ashtekar, J.C. Baez, and K. Krasnov, Adv. Theor. Math. Phys.4,1 (2000).
[197]J. R. David, G. Mandal, and S. R. Wadia, Phys. Rep.369,549 (2002).
[198]T. Damour, arXiv:hep-th/0401160.
[199]W. H. Zurek, Phys. Rev. Lett.49,1683 (1982).
[200]D. Page, Phys. Rev. D 13,198 (1976); Phys. Rev. Lett.50,1013 (1983).
[201]B. W. Schumacher, Phys. Rev. Lett.54,2643 (1985).
[202]A. Barrau, J. Grain, and C. Weydert, Phys. Rev. D 76,087503 (2007).
[203]F. R. Tangherlini, Nuovo. Cim.27,636 (1963).
[204]H. Nariai, Sci. Rep. Tohoku Univ. Ser. Ⅰ 35,62 (1951).
[205]S. Nojiri and S. D. Odintsov, Phys. Rev. D 59,044026 (1999).
[206]Y. S. Myung, Phys. Lett. B645,369 (2007).
[207]R. Bousso and S. W. Hawking, Phys. Rev. D 54,6312 (1996).
[208]R. M. Wald, Commun. Math. Phys.45,9 (1975).
[209]S. W. Hawking, Phys. Rev. D 14,2460 (1976).
[210]M. A. Rubin and C. R. Ordonez, J. Math. Phys.25,2888 (1984); 26,65 (1985).
[211]E. Newman and R. Penrose, J. Math. Phys.3,566 (1962).
[212]D. Ida, K. y. Oda, and S. C. Park, Phys. Rev. D 67,064025 (2003); 69,049901(E) (2004); 71,124039 (2005).
[213]J. N. Goldberg et al., J. Math. Phys.8,2155 (1967).
[214]A. Ishibashi and H. Kodama, Prog. Theor. Phys.110,701 (2003); 111,29 (2004).
[215]S. Creek,0. Efthimiou, P. Kanti, and K. Tamvakis, Phys. Lett. B635,39 (2006).
[216]V. Cardoso, M. Cavaglia, and L. Gualtieri, J. High Energy Phys.02,021 (2006).
[217]N. Sanchez, Phys. Rev. D 18,1030 (1978).
[218]E. Jung and D. K. Park, Class. Quant. Grav.21,3717 (2004); Nucl. Phys. B717, 272 (2005).
[219]M. Cvetic and F. Larsen, Phys. Rev. D 57,6297 (1998).
[220]C. M. Harris and P. Kanti, J. High Energy Phys.10,014 (2003).
[221]F. J. Zerilli, Phys. Rev. Lett.24,737 (1970).
[222]C. V. Vishveshwara, Nature 227,936 (1970).
[223]S. Chandrasekhar, The Mathematical Theory of Black Hole (Oxford University Press, New York,1983).
[224]D. K. Park, Phys. Lett. B638,246 (2006).
[225]Y. S. Myung, Phys. Rev. D 77,104007 (2008).
[226]R. C. Myers and M. J. Perry, Ann. Phys.172,304 (1986).
[227]J. Y. Shen, B. Wang, and R. K. Su, Phys. Rev. D 74,044036 (2006).
[228]E. Abdalla, B. Cuadros-Melgar, A. B. Pavan, and C. Molina, Nucl. Phys. B752, 40 (2006).
[229]L. Liu, B. Wang, G. Yang, Phys. Rev. D 76,064014 (2007).
[230]W. Israel, Phys. Rev.164,1776 (1967).
[231]B. Carter, Phys. Rev. Lett.26,331 (1971).
[232]S. W. Hawking, Commun. Math. Phys.25,152 (1972).
[233]D. C. Robinson, Phys. Rev. Lett.34,905 (1975).
[234]G. W. Gibbons, D. Ida, and T. Shiromizu, Phys. Rev. Lett.89,041101 (2002); Prog. Theor. Phys. Suppl.148,284 (2003).
[235]C. V. Vishveshwara, Phys. Rev. D 1,2870 (1970).
[236]R. Gregory and R. Laflamme, Phys. Rev. Lett.70,2837 (1993); Nucl. Phys. B428, 399 (1994).
[237]T. Harmark, V. Niarchos, and N. A. Obers, Class. Quant. Grav.24, Rl (2007).
[238]R. Gregory, Class. Quantum Grav.17, L125 (2000).
[239]V. E. Hubeny and M. Rangamani, J. High Energy Phys.05,027 (2002).
[240]T. Hollowood, S. P. Kumar, and A. Naqvi, J. High Energy Phys.01,001 (2007).
[241]K. Murata, Prog. Theor. Phys.121,1099 (2009) [arXiv:0812.0718].
[242]M. M. Caldarelli, R. Emparan, and M. J. Rodriguez, J. High Energy Phys.11,011 (2008).
[243]T. Delsate, Phys. Lett. B663,118 (2008).
[244]T. Hirayama and G. Kang, Phys. Rev. D 64,064010 (2001).
[245]S. Yin et. al., arXiv:1004.4244, submitted to Phys. Rev. D.
[246]B. Kol, arXiv.hep-th/0208056.
[247]B. Kol, J. High Energy Phys.10,049 (2005).
[248]B. Kol, Phys. Rept.422,119 (2006).
[249]V. Niarchos, Mod. Phys. Lett. A 23,2625 (2008).
[250]L. Vanzo, Phys. Rev. D 56,6475 (1997).
[251]B. Wang, E. Abdalla, and R. B. Mann, Phys. Rev. D 65,084006 (2002).
[252]S. Chen, K. Schleich, and D. M. Witt, Phys. Rev. D 78,126001 (2008).
[253]Y. Brihaye, T. Delsate and E. Radu, Phys. Lett. B662,264 (2008).
[254]S. S. Gubser and I. Mitra, J. High Energy Phys.08,018 (2001).
[255]D. Marolf and B. C. Palmer, Phys. Rev. D 70,084045 (2004).
[256]J. J. Friess, S. S. Gubser, and I. Mitra, Phys. Rev. D 72,104019 (2005).
[257]G. T. Horowitz and V. E. Hubeny, Phys. Rev. D 62,024027 (2000).
[258]B. Wang, C. Y. Lin, and E. Abdalla, Phys. Lett. B481,79 (2000).
[259]B. Wang, C. Molina, and E. Abdalla, Phys. Rev. D 63,084001 (2001).
[260]J. M. Zhu, B. Wang, and E. Abdalla, Phys. Rev. D 63,124004 (2001).
[261]V. Cardoso and J. P. S. Lemos, Phys. Rev. D 63,124015 (2001); 64,084017 (2001).
[262]E. Berti and K. D. Kokkotas, Phys. Rev. D 67,064020 (2003).
[263]L. Liu and B. Wang, Phys. Rev. D 78,064001 (2008).
[264]M. Maggiore, Phys. Rev. Lett.100,141301 (2008).
[265]S. W. Hawking and D. N. Page, Commun. Math. Phys.87,577 (1983).
[266]A. G. Riess et. al., Astronphys. J.116,1009 (1998).
[267]S. Perlmutter et. al., Astrophys. J.517,565 (1999).
[268]A. G. Riess et. al., Astrophys. J.560,49 (2001).
[269]S. Weinberg, Rev. Mod. Phys.61,1 (1989).
[270]R. R. Caldwell, R. Dave, and P. J. Steinhardt, Phys. Rev. Lett.80,1582 (1998).
[271]P. J. E. Peebles and A. Vilenkin, Phys. Rev. D 59,063505 (1999).
[272]P. J. Steinhardt, L. M. Wang, and I. Zlatev, Phys. Rev. D 59,123504 (1999).
[273]M. Doran and J. Jaeckel, Phys. Rev. D 66,043519 (2002).
[274]A. Y. Kamenshchik, U. Moschella, and V. Pasquier, Phys. Lett. B511,256 (2001).
[275]M. Li, Phys. Lett. B603,1 (2004); Q. G. Huang and M. Li, JCAP 08,013 (2004).
[276]R. R. Caldwell, Phys. Lett. B545,23 (2002).
[277]R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett.91, 071301 (2003).
[278]J. M. Cline, S. Y. Jeon, and G. D. Moore, Phys. Rev. D 70,043543 (2004).
[279]U. Alam, V. Sahni, and A. Starobinsky, JCAP 06,008 (2004).
[280]U. Alam, V. Sahni, T. Saini, and A. Starobinsky, Mon. Not. Roy. Astron. Soc.354, 275 (2004).
[281]R. Daly and S. Djorgovski, Astrophys. J.612,652 (2004).
[282]B. Wang, C. Y. Lin, and C. Molina, Phys. Rev. D 70,064025 (2004).
[283]Y. Wang and M. Tegmark, Phys. Rev. D 71,103513 (2005).
[284]Y. G. Gong, Class. Quant. Grav.22,2121 (2005).
[285]T. Choudhury and T. Padmanabhan, Astron. Astrophys.429,807 (2005).
[286]B. Feng, X. L.Wang, and X. M. Zhang, Phys. Lett. B607,35 (2005).
[287]W. Hu, Phys. Rev. D 71,047301 (2005).
[288]Z. K. Guo, Y. S. Piao, X. M. Zhang, and Y. Z. Zhang, Phys. Lett. B608,177 (2005).
[289]X. F. Zhang, H. Li, Y. S. Piao, and X. Zhang, Mod. Phys. Lett. A 21,231 (2006).
[290]M. Z. Li, B. Feng, and X. M. Zhang, JCAP 12,002 (2005).
[291]S. Nojiri and S. D. Odintsov, Phys. Lett. B562,147 (2003); Phys. Rev. D 70, 103522 (2004).
[292]S. Nojiri, S. D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71,063004 (2005).
[293]A. Vikman, Phys. Rev. D 71,023515 (2005).
[294]A. Anisimov, E. Babichev, and A. Vikman, JCAP 06,006 (2005).
[295]P. Singh, Class. Quant. Grav.22,4203 (2005).
[296]H. Stefancic, Phys. Rev. D 71,124036 (2005).
[297]B. Wang, Y. Gong, and E. Abdalla, Phys. Lett. B624,141 (2006).
[298]B. Wang, C. Y. Lin, and E. Abdalla, Phys. Lett. B637,357 (2006).
[299]B. Wang, J. D. Zang, C. Y. Lin, E. Abdalla and S. Micheletti, Nucl. Phys. B778, 69 (2007).
[300]E.O. Kahya and V. K. Onemli, Phys. Rev. D 76,043512 (2007).
[301]T. Koivisto and D. F. Mota, Phys. Lett. B644,104 (2007); Phys. Rev. D 75, 023518 (2007).
[302]G. R. Randall and R. Sundrum, Phys. Rev. Lett.83,3370 (1999); Phys. Rev. Lett. 83,4690 (1999).
[303]E. Kiritsis, N. Tetradis, and T. N. Tomaras, J. High Energy Phys.03,019 (2002).
[304]E. Kiritsis, G. Kofinas, N. Tetradis, T. N. Tomaras, and V. Zarikas, J. High Energy Phys.02,035 (2003).
[305]E. Kiritsis, JCAP 10,014 (2005).
[306]P. S. Apostolopoulos and N. Tetradis, Phys. Rev. D 71,043506 (2005); Phys. Lett. B633,409 (2006).
[307]K. I. Umezu et al., Phys. Rev. D 73,063527 (2006).
[308]R. G. Cai, Y. Gong, and B. Wang, JCAP 03,006 (2006).
[309]P. S. Apostolopoulos and N. Tetradis, Phys. Rev. D 74,064021 (2006).
[310]C. Bogdanos and K. Tamvakis, Phys. Lett. B646,39 (2007); C. Bogdanos, A. Dimitridis, and K. Tamvakis, Phys. Rev. D 75,087303 (2007).
[311]A. Sheykhi, B. Wang, and N. Riazi, Phys. Rev. D 75,123513 (2007).
[312]D. Lovelock, J. Math. Phys.12,498 (1971).
[313]B. Zwiebach, Phys. Lett. B156,315 (1985).
[314]D. G. Boulware and S. Deser, Phys. Rev. Lett.55,2656 (1985).
[315]G. Kofinas, R. Maartens, and E. Papantonopoulos, J. High Energy Phys.10,066 (2003).
[316]G. Dvali, G. Gabadadze, and M. Porrati, Phys. Lett. B485,208 (2000).
[317]G. Kofinas, G. Panotopoulos, and N. Tomaras, J. High Energy Phys.01,107 (2006).
[318]R. A. Brown, R. Maartens, E. Papantonopoulos, and V. Zamarias, JCAP 11,008 (2005).
[319]R. G. Cai, H. S. Zhang, and A. Wang, Commun. Theor. Phys.44,948 (2005).
[320]S. Yin, B. Wang, E. Abdalla, and C. Y. Lin, Phys. Rev. D 76,124026 (2007).
[321]C. Deffayet, Phys. Lett. B502,199 (2001).
[322]C. Barcelo, C. Germani, and C. F. Sopuerta, Phys. Rev. D 68,104007 (2003).
[323]R. Maartens, Phys. Rev. D 62,084023 (2000).
[324]D. N. Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl.148,175 (2003).
[325]E. V. Linder and A. Jenkins, Mon. Not. Roy. Astron. Soc.346,573 (2003).
[326]R. Jimenez, L. Verde, T. Treu, and D. Stern, Astrophys. J.593,622 (2003).
[327]J. Simon, L. Verde, and R. Jimenez, Phys. Rev. D 71,123001 (2005).
[328]W. L. Freedman, et al., Astrophys. J.553,47 (2001).
[329]J. H. He, B. Wang, and E. Papantonopoulos, Phys. Lett. B654,133, (2007).
[2]G. E. Brown and M. Rho, Phys. Rev. Lett 66,2720 (1991).
[3]K. Saito, K. Tsushima and A. W. Thomas, Phys. Rev. C 56,566 (1997).
[4]G. J. Lolos et. al., Phys. Rev. Lett.80,241 (1998).
[5]G. N. Fowler, S. Raha and R. M. Weiner, Z. Phys. C 9,271 (1981).
[6]V. Goloviznin and H. Satz, Z. Phys. C 57,671 (1993).
[7]A. Peshier, B. Kampfer,0. P. Pavlenko, and G. Soff, Phys. Lett. B337,235 (1994).
[8]M. I. Gorenstein and S. N. Yang, Phys. Rev. D 52,5206 (1995).
[9]M. Bluhm, B. Kampfer, and G. Soff, Phys. Lett. B620,131 (2005).
[10]V. M. Bannur, Phys. Lett. B647,271 (2007); Phys. Rev. C 75,044905 (2007).
[11]S. Chakrabarty, S. Raha, and B. Sinha, Phys. Lett. B229,112 (1989).
[12]S. Chakrabarty, Phys. Rev. D 43,627 (1991).
[13]S. Chakrabarty, Phys. Rev. D 48,1409 (1993).
[14]O. G. Benvenuto and G. Lugones, Phys. Rev. D 51,1989 (1995).
[15]G. Lugones and O. G. Benvenuto, Phys. Rev. D 52,1276 (1995).
[16]G. X. Peng, H. C. Chiang, P. Z. Ning, and B. S. Zou, Phys. Rev. C 59,3452 (1999).
[17]G. X. Peng et al., Phys. Rev. C 62,025801 (2000).
[18]P. Wang, Phys. Rev. C 62,015204 (2000).
[19]Y. Zhang, R. K. Su, S. Q. Ying, and P. Wang, Euro. Phys. Lett.56,361 (2001).
[20]Y. Zhang and R. K. Su, Phys. Rev. C 65,035202 (2002).
[21]Y. Zhang and R. K. Su, Phys. Rev. C 67,015202 (2003).
[22]X. J. Wen et al., Phys. Rev. C 72,015204 (2005).
[23]C. Wu, W. L. Qian and R. K. Su, Phys. Rev. C 72,035205 (2005); Chin. Phys. Lett.22,1866 (2005).
[24]H. Mao, R. K. Su, and W. Q. Zhao, Phys. Rev. C 74,055204 (2006).
[25]S. Yin and R. K. Su, Phys. Rev. C 77,055204 (2008).
[26]S. Yin and R. K. Su, Int. J. Mod. Phys. A,25,1449 (2010).
[27]A. Das, Finite Temperature Field Theory (World Scientific, Singapore,1997).
[28]J. P. Blaizot, E. Iancu, and A. Rebhan, Phys. Rev. D 63,065003 (2001).
[29]Y. J. Zhang, S. Gao, and R. K. Su, Phys. Rev. C 56,3336 (1997).
[30]H. Shiomi and T. Hatsuda, Phys. Lett. B334,281 (1994).
[31]V. K. Gupta, A. Gupta, S. Singh, and J. D. Anand, Int. J. Mod. Phys. D 12,583 (2003).
[32]J. Y. Shen, Y. Zhang, B. Wang, and R. K. Su, Int. J. Mod. Phys. A 20,7547 (2005).
[33]E. Farhi and R. L. Jaffe, Phys. Rev, D 30,2379 (1984).
[34]J. Adams et al. [STAR Collaboration], Nucl. Phys. A757,102 (2005).
[35]K. Adcox et al. [PHENIX Collaboration], Nucl. Phys. A757,184 (2005).
[36]T. S. Biro, A. A. Shanenko, and V. D. Toneev, Phys. Atom. Nucl.66,982 (2003).
[37]J. Engels et al., Z. Phys. C 42,341 (1989).
[38]G. Boyd et al., Phys. Rev. Lett.75,4169 (1995); Nucl. Phys. B469,419 (1996).
[39]J. Schaffner, C. Greiner,and H. Stoecker, Phys. Rev. C 46,322 (1992).
[40]C. Greiner and J. Schaffner-Bielich, "Physics of strange matter", "Heavy Elements and Related New Phenomena", Vol Ⅱ, p1074, by R. K. Gupta and W. Greiner, World Scientific Publications (1999). [arXiv:nucl-th/9801062]
[41]N. K. Glendenning, Phys. Rev. C 23,2757 (1981).
[42]P. Papazoglou et al., Phys. Rev. C 57,2576 (1998).
[43]P. Papazoglou et al., Phys. Rev. C 59,411 (1999).
[44]J. Schaffner et al., Phys. Rev. Lett.71,1328 (1993).
[45]J. Schaffner et al., Annals Phys.235,35 (1994).
[46]J. Schaffner and A. Gal, Phys. Rev. C 62,034311 (2000).
[47]K. Saito and A. W. Thomas, Phys. Lett. B327,9 (1994).
[48]P. Wang, R. K. Su, H. Q. Song, and L. L. Zhang, Nucl. Phys. A653,166 (1999).
[49]R. J. Furnstahl, H. B. Tang, and B. D. Serot, Phys. Rev. C 52,1368 (1995); R. J. Furnstahl, B. D. Serot, and H. B. Tang, Nucl. Phys. A598,539 (1996); ibid. A615, 441 (1997).
[50]M. Danysz et al., Nucl. Phys.49,121 (1963).
[51]R. H. Dalitz et al., Proc. Rol. Soc. Ser. A 426,1 (1989).
[52]C. Beckmann et al., Phys. Rev. C 65,024301 (2002).
[53]L. Yang, W. L. Qian, R. K. Su, and H. Q. Song, Phys. Rev. C 70,045207 (2004).
[54]P. Wang, D. B. Leinweber, A. W. Thomas, and A. G. Williams, Phys. Rev. C 70, 055204 (2004).
[55]H. Takahashi et al, Phys. Rev. Lett.87,212502 (2001).
[56]D. J. Prowse, Phys. Rev. Lett.17,282 (1966).
[57]S. Aoki et al., Prog. Theor. Phys.85,1287 (1991).
[58]C. B. Dover, D. J. Millener, A. Gal, and D. H. Davis, Phys. Rev. C 44,1905 (1991).
[59]H. Q. Song, R. K. Su, D. H. Lu, and W. L. Qian, Phys. Rev. C 68,055201 (2003).
[60]W. L. Qian, R. K. Su, and H. Q. Song, J. Phys. G 30,1893 (2004).
[61]L. L. Zhang, H. Q. Song, P. Wang, and R. K. Su, J. Phys. G 26,1301 (2000).
[62]W. L. Qian, R. K. Su, and H. Q. Song, Commun. Theor. Phys.40,466 (2003).
[63]H. J. Schulze et al., Phys. Rev. C 57,704 (1998).
[64]Y. Zhang and R. K. Su, Mod. Phys. Lett. A 18,143 (2003).
[65]L. Yang, S. Yin, W. Qian, and R. K. Su, Phys. Rev. C 73,025203 (2006).
[66]H. Muller and B. D. Serot, Phys. Rev. C 52,2072 (1995).
[67]W. L. Qian, R. K. Su, and P. Wang, Phys. Lett. B491,90 (2000).
[68]W. L. Qian, R. K. Su, and H. Q. Song, Phys. Lett. B520,217 (2001).
[69]W. L. Qian, R. K. Su, and H. Q. Song, J. Phys. G 28,379 (2002).
[70]W. L. Qian and R. K. Su, J. Phys. G 29,1023 (2003).
[71]D. J. Millener, A. Gal, C. B. Dover, and R. H. Dalitz, Phys. Rev. C 31,499 (1985).
[72]V. M. Kolomietz, A. I. Sanzhur, S. Shlomo, and S. A. Firin, Phys. Rev. C 64,024315 (2001).
[73]L. G. Moretto et al., Phys. Rev. Lett.76,2822 (1996).
[74]Y. G. Ma et al., Phys. Rev. C 69,031604(R) (2004).
[75]Y. G. Ma et al., Phys. Rev. C 71,054606 (2005).
[76]T. Sil, S. K. Samaddar, J. N. De, and S. Shlomo, Phys. Rev. C 69,014602 (2004).
[77]A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins, Nature, 217,709 (1968).
[78]D. G. Ravenhall and C. J. Pethick, Astrophys. J.424,846 (1994).
[79]V. Kalogera and D. Psaltis, Phys. Rev. D 61,024009 (1999).
[80]M. Prakash et al., Phys. Rep.280,1 (1997).
[81]S. Gupta et al., Astrophys. J.662,1188 (1971).
[82]G. Baym, C. Pethick, and P. Sutherland, Astrophys. J.170,299 (1971).
[83]N. K. Glendenning, Astrophys. J.293,470 (1985).
[84]C. Wu and R. K. Su, J. Phys. G 36,095101 (2009).
[85]J. M. Lattimer and M. Prakash, Astrophys. J.550,426 (2001).
[86]T. Klahn et al., Phys. Rev. C 74,035802 (2006).
[87]J. M. Lattimer and M. Prakash, Phys. Rep.442,109 (2007).
[88]E. Witten, Phys. Rev. D 30,272 (1984).
[89]P. Haensel, J. L. Zdunik, and R. Schaefer, Astron. Astrophys.160,121 (1986).
[90]C. Alcock, E. Farhi, and A. Olinto, Astrophys. J.310,261 (1986).
[91]R. X. Xu, Astrophys. J.596, L59 (2003).
[92]F. Weber, Prog. Part. Nucl. Phys.54,193 (2005).
[93]V. A. Ambartsumyan and G. S. Saakyan, Soviet Astr.-AJ 4,187 (1960).
[94]N. K. Glendenning, Phys. Lett. B114,392 (1982).
[95]J. Schaffner and I. N. Mishustin, Phys. Rev. C 53,1416 (1996).
[96]M. Baldo, G. F. Burgio, and H.-J. Schulze, Phys. Rev. C 58,3688 (1998); ibid.61, 055801 (2000).
[97]P. Wang, Z. Y. Zhang, Y. W. Yu, R. K. Su, and H. Q. Song, Nucl. Phys. A688,791 (2001).
[98]P. Wang, H. Guo, Z. Y. Zhang, Y. W. Yu, R. K. Su, and H. Q. Song, Nucl. Phys. A705,455 (2002).
[99]P. Wang, S. Lawley, D. B. Leinweber, A. W. Thomas, and A. G. Williams, Phys. Rev. C 72,045801 (2005).
[100]P. C. C. Champion, arXiv:0907.3219.
[101]S. Yin, J. Zang and R. K. Su, Eur. Phys. J. A 43,295 (2010).
[102]J. B. Hartle, Astrophys. J.150,1005 (1967); J. B. Hartle and K. S. Thorne, Astrophys. J.153,807 (1968).
[103]T. Regge and J. A. Wheeler, Phys. Rev.108,1063 (1957).
[104]J. M. Lattimer and M. Prakash, Science,304,536 (2004).
[105]P. W. Anderson and N. Itoh, Nature 256,25 (1975).
[106]N. K. Glendenning and F. Weber, Astrophys. J.400,647 (1992).
[107]J. L. Zdunik, P. Haensel, and E. Gourgoulhon, Astron. Astrophys.,372,535 (2001).
[108]J. W. Negele and D. Vautherin, Nucl. Phys. A207,298 (1974).
[109]S. B. Ruster, M. Hempel, and J. Schaffner-Bielich, Phys. Rev. C 73,035804 (2006).
[110]F. Weber and N. K. Glendenning, Astrophys. J.390,541 (1992).
[111]M. Hanauske et al., Astrophys. J.537,958 (2000).
[112]S. Schramm and D. Zschiesche, J. Phys. G 29,531 (2003).
[113]G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Astrophys. J.398,203 (1992); ibid.422,227 (1994).
[114]T. W. Baumgarte, S. L. Shapiro, and M. Shibata, Astrophys. J.528, L29 (2000).
[115]N. D. Lyford, T. W. Baumgarte, and S. L. Shapiro, Astrophys. J.583,410 (2003).
[116]I. A. Morrison, T. W. Baumgarte, and S. L. Shapiro, Astrophys. J.610,941 (2004).
[117]G. F. Burgio, H.-J. Schulze, and F. Weber, Astron. Astrophys.408,675 (2003).
[118]Baldo et al., arxiv:astro-ph/0312446.
[119]N. K. Glendenning, Phys. Rev. D 46,1274 (1992).
[120]A. Rosenhauer et al., Nucl. Phys. A540,630 (1992).
[121]F. Weber, J. Phys. G 25, R195 (1999).
[122]M. Alford et al., Nature 455, E7 (2007).
[123]L. McLerran and R. D. Pisarski, Nucl. Phys. A796,83 (2007).
[124]L. Ya. Glozman and R. F. Wagenbrunn, Phys. Rev. D 77,054027 (2008).
[125]A. H. Guth, Phys. Rev. D 23,347 (1981).
[126]A. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur, Switzerland,1990), arXiv:hep-th/0503203.
[127]A.R. Liddle and D.H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge,.England,2000).
[128]R. Easther, B. R. Greene, W. H. Kinney, and G. Shiu, Phys. Rev. D 64,103502 (2001).
[129]R. Easther, B. R. Greene, W. H. Kinney, and G. Shiu, Phys. Rev. D 66,023518 (2002).
[130]U. F. Danielsson, Phys. Rev. D 66,023511 (2002).
[131]B. Wang, L. H. Xue, Z. Zhang, and W-Y. P Hwang, Phys. Rev. D 67,123519 (2003).
[132]K. Goldstein and D. A. Lowe, Phys. Rev. D 67,063502 (2003).
[133]J. Martin and C. Ringeval, Phys. Rev. D 69,083515 (2004); ibid.127303 (2004).
[134]J. Martin and C. Ringeval, J. Cosmol. Astropart. Phys.01,007 (2005); ibid.08, 009 (2006).
[135]J. Ren, H.-G. Zhang, and X.-H. Meng, Int. J. Mod. Phys. D 18,1343 (2009).
[136]N. E. Groeneboom and (?)stein Elgar(?)y, Phys. Rev. D 77,043522 (2008).
[137]U. H. Danielsson, J. High Energy Phys.12,025 (2002).
[138]R. H. Brandenberger, hep-th/0210186.
[139]X. Wang, B. Feng, and M. Li, Int. J. Mod. Phys. D 14,1347 (2005).
[140]C. P. Burgess, J. M. Cline, F. Lemieux, and R. Holman, J. High Energy Phys.02, 048 (2003).
[141]N. A. Chernikov and E. A. Tagirov, Ann. Inst. Henri Poincare, vol. Ⅸ,2,109 (1968).
[142]E. Mottola, Phys. Rev. D 31,754 (1985).
[143]B. Allen, Phys. Rev. D 32,3136 (1985).
[144]R. Floreanini, C. T. Hill, and R. Jackiw, Ann. Phys. (NY) 175,345 (1987).
[145]R. Bousso, A. Maloney, and A. Strominger, Phys. Rev. D 65,104039 (2002).
[146]M. Spradlin and A. Volovich, Phys. Rev. D 65,104037 (2002).
[147]A. H. Guth and S.-Y. Pi, Phys. Rev. D 32,1899 (1985).
[148]K. Bhattacharya, S. Mohanty, and R. Rangarajan, Phys. Rev. Lett.96,121302 (2006); ibid.97,231301 (2006).
[149]S. Yin, B. Wang, R. K. Su, Phys. Lett. B675,84 (2009).
[150]H. Umezawa, H. Matsumoto, and M. Tachiki. Thermo field dynamics and condensed states (North-Holland, Amsterdam,1982).
[151]L. Bergstrom and U. F. Danielsson, J. High Eenergy Phys.12,038 (2002).
[152]G. Hinshaw et al., Astrophys. J. Suppl.180,225 (2009).
[153]K. Enqvist, M. S. Sloth, Phys. Rev. Lett.93,221302 (2004); K. Enqvist, S. Hannes-tad, and M. S. Sloth, JCAP 02,004 (2005).
[154]J. Shen, B. Wang, E. Abdalla, and R.-K. Su, Phys. Lett. B609,200 (2005).
[155]A. G. Cohen, A.B. Kaplan, and A. E. Nelson, Phys. Rev. Lett 82,4971 (1999).
[156]M. Giovanini, Int. J. Mod. Phys. D 14,363 (2005).
[157]T. Banks and W. Fischler, hep-th/9906038.
[158]S. Dimopoulos and G. Landsberg, Phys. Rev. Lett.87,161602 (2001).
[159]S. B. Giddings and S. Thomas, Phys. Rev. D 65,056010 (2002).
[160]V. Cardoso, J. P. S. Lemos, and S. Yoshida, Phys. Rev. D 69,044004 (2004).
[161]D. Stojkovic, Phys. Rev. Lett.94,011603 (2005).
[162]R. d. Rocha, C. H. Coimbra-Araujo, Phys. Rev. D 74,055006 (2006).
[163]M. Cavaglia, R. Godang, L. M. Cremaldi, D. J. Summers, J. High Energy Phys. 06,055 (2007).
[164]A. Goyal, A. Gupta, and N. Mahajan, Phys. Rev. D 63,043003 (2001).
[165]J. L. Feng and A. D. Shapere, Phys. Rev. Lett.88,021303 (2002).
[166]E. J. Ahn, M. Ave, M. Cavaglia, and A.V. Olinto, Phys. Rev. D 68,043004 (2003).
[167]T. Han and D. Hooper, New J. Phys.6,150 (2004).
[168]A. Cafarella, C. Coriano, and T. N. Tomaras, J. High Energy Phys.06,065 (2005).
[169]D. Stojkovic and G. D. Starkman, Phys. Rev. Lett.96,041303 (2006).
[170]L. A. Anchordoqui, M. M. Glenz, and L. Parker, Phys. Rev. D 75,024011 (2007).
[171]P. Kanti, Int. J. Mod. Phys. A 19,4899 (2004).
[172]A. Barrau, J. Grain, and S. O. Alexeyev, Phys. Lett. B584,114 (2004).
[173]J. Grain, A. Barrau, and P. Kanti, Phys. Rev. D 72,104016 (2005).
[174]P. Kanti, J. Grain and A. Barrau, Phys. Rev. D 71,104002 (2005).
[175]J. Maldacena, Adv. Theor. Math. Phys.2,231 (1998).
[176]S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B428,105 (1998).
[177]E. Witten, Adv. Theor. Math. Phys.2,253 (1998).
[178]A. G. Riess et al., Astrophys. J.659,98 (2007).
[179]G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15,2738 (1977).
[180]R. L. Mallett, Phys. Rev. D 3,2201 (1986).
[181]P. C. W. Davies, L. H. Ford, and D. N. Page, Phys. Rev. D 34,1700 (1986).
[182]W. H. Huang, Class. Quant. Grav.9,1199 (1992).
[183]R. Bousso and S. W. Hawking, Phys. Rev. D 57,2436 (1998).
[184]O. J. C. Dias and J. P. S. Lemos, Phys. Rev. D 70,124023 (2004).
[185]A. J. M. Medved, Phys. Rev. D 66,124009 (2002).
[186]V. Balasubramanian, J. de Boer, and D. Minic, Phys. Rev. D 65,123508 (2002).
[187]R. G. Cai, Y. S. Myung, and Y. Z. Zhang, Phys. Rev. D 65,084019 (2002).
[188]A. M. Ghezelbach and R. B. Mann, J. High Energy Phys.01,005 (2002).
[189]C. Molina, Phys. Rev. D 68,064007 (2003).
[190]V. Cardoso, O. J. C. Dias and J. P. S. Lemos, Phys. Rev. D 70,024002 (2004).
[191]J. Natario and R. Schiappa, Adv. Theor. Math. Phys.8,1001 (2004).
[192]J. Labbe, A. Barrau, and J. Grain, Proc. Sci., HEP2005,013 (2006) [arXiv:hep-ph/0511211].
[193]T. Harmark, J. Natario, and R. Schiappa, arXiv:0708.0017.
[194]S. F. Wu, S. Yin, G. H. Yang, and P. M. Zhang, Phys. Rev. D 78,084010 (2008).
[195]J.D. Bekenstein, Phys. Rev. D 7,2333 (1973).
[196]A. Ashtekar, J.C. Baez, and K. Krasnov, Adv. Theor. Math. Phys.4,1 (2000).
[197]J. R. David, G. Mandal, and S. R. Wadia, Phys. Rep.369,549 (2002).
[198]T. Damour, arXiv:hep-th/0401160.
[199]W. H. Zurek, Phys. Rev. Lett.49,1683 (1982).
[200]D. Page, Phys. Rev. D 13,198 (1976); Phys. Rev. Lett.50,1013 (1983).
[201]B. W. Schumacher, Phys. Rev. Lett.54,2643 (1985).
[202]A. Barrau, J. Grain, and C. Weydert, Phys. Rev. D 76,087503 (2007).
[203]F. R. Tangherlini, Nuovo. Cim.27,636 (1963).
[204]H. Nariai, Sci. Rep. Tohoku Univ. Ser. Ⅰ 35,62 (1951).
[205]S. Nojiri and S. D. Odintsov, Phys. Rev. D 59,044026 (1999).
[206]Y. S. Myung, Phys. Lett. B645,369 (2007).
[207]R. Bousso and S. W. Hawking, Phys. Rev. D 54,6312 (1996).
[208]R. M. Wald, Commun. Math. Phys.45,9 (1975).
[209]S. W. Hawking, Phys. Rev. D 14,2460 (1976).
[210]M. A. Rubin and C. R. Ordonez, J. Math. Phys.25,2888 (1984); 26,65 (1985).
[211]E. Newman and R. Penrose, J. Math. Phys.3,566 (1962).
[212]D. Ida, K. y. Oda, and S. C. Park, Phys. Rev. D 67,064025 (2003); 69,049901(E) (2004); 71,124039 (2005).
[213]J. N. Goldberg et al., J. Math. Phys.8,2155 (1967).
[214]A. Ishibashi and H. Kodama, Prog. Theor. Phys.110,701 (2003); 111,29 (2004).
[215]S. Creek,0. Efthimiou, P. Kanti, and K. Tamvakis, Phys. Lett. B635,39 (2006).
[216]V. Cardoso, M. Cavaglia, and L. Gualtieri, J. High Energy Phys.02,021 (2006).
[217]N. Sanchez, Phys. Rev. D 18,1030 (1978).
[218]E. Jung and D. K. Park, Class. Quant. Grav.21,3717 (2004); Nucl. Phys. B717, 272 (2005).
[219]M. Cvetic and F. Larsen, Phys. Rev. D 57,6297 (1998).
[220]C. M. Harris and P. Kanti, J. High Energy Phys.10,014 (2003).
[221]F. J. Zerilli, Phys. Rev. Lett.24,737 (1970).
[222]C. V. Vishveshwara, Nature 227,936 (1970).
[223]S. Chandrasekhar, The Mathematical Theory of Black Hole (Oxford University Press, New York,1983).
[224]D. K. Park, Phys. Lett. B638,246 (2006).
[225]Y. S. Myung, Phys. Rev. D 77,104007 (2008).
[226]R. C. Myers and M. J. Perry, Ann. Phys.172,304 (1986).
[227]J. Y. Shen, B. Wang, and R. K. Su, Phys. Rev. D 74,044036 (2006).
[228]E. Abdalla, B. Cuadros-Melgar, A. B. Pavan, and C. Molina, Nucl. Phys. B752, 40 (2006).
[229]L. Liu, B. Wang, G. Yang, Phys. Rev. D 76,064014 (2007).
[230]W. Israel, Phys. Rev.164,1776 (1967).
[231]B. Carter, Phys. Rev. Lett.26,331 (1971).
[232]S. W. Hawking, Commun. Math. Phys.25,152 (1972).
[233]D. C. Robinson, Phys. Rev. Lett.34,905 (1975).
[234]G. W. Gibbons, D. Ida, and T. Shiromizu, Phys. Rev. Lett.89,041101 (2002); Prog. Theor. Phys. Suppl.148,284 (2003).
[235]C. V. Vishveshwara, Phys. Rev. D 1,2870 (1970).
[236]R. Gregory and R. Laflamme, Phys. Rev. Lett.70,2837 (1993); Nucl. Phys. B428, 399 (1994).
[237]T. Harmark, V. Niarchos, and N. A. Obers, Class. Quant. Grav.24, Rl (2007).
[238]R. Gregory, Class. Quantum Grav.17, L125 (2000).
[239]V. E. Hubeny and M. Rangamani, J. High Energy Phys.05,027 (2002).
[240]T. Hollowood, S. P. Kumar, and A. Naqvi, J. High Energy Phys.01,001 (2007).
[241]K. Murata, Prog. Theor. Phys.121,1099 (2009) [arXiv:0812.0718].
[242]M. M. Caldarelli, R. Emparan, and M. J. Rodriguez, J. High Energy Phys.11,011 (2008).
[243]T. Delsate, Phys. Lett. B663,118 (2008).
[244]T. Hirayama and G. Kang, Phys. Rev. D 64,064010 (2001).
[245]S. Yin et. al., arXiv:1004.4244, submitted to Phys. Rev. D.
[246]B. Kol, arXiv.hep-th/0208056.
[247]B. Kol, J. High Energy Phys.10,049 (2005).
[248]B. Kol, Phys. Rept.422,119 (2006).
[249]V. Niarchos, Mod. Phys. Lett. A 23,2625 (2008).
[250]L. Vanzo, Phys. Rev. D 56,6475 (1997).
[251]B. Wang, E. Abdalla, and R. B. Mann, Phys. Rev. D 65,084006 (2002).
[252]S. Chen, K. Schleich, and D. M. Witt, Phys. Rev. D 78,126001 (2008).
[253]Y. Brihaye, T. Delsate and E. Radu, Phys. Lett. B662,264 (2008).
[254]S. S. Gubser and I. Mitra, J. High Energy Phys.08,018 (2001).
[255]D. Marolf and B. C. Palmer, Phys. Rev. D 70,084045 (2004).
[256]J. J. Friess, S. S. Gubser, and I. Mitra, Phys. Rev. D 72,104019 (2005).
[257]G. T. Horowitz and V. E. Hubeny, Phys. Rev. D 62,024027 (2000).
[258]B. Wang, C. Y. Lin, and E. Abdalla, Phys. Lett. B481,79 (2000).
[259]B. Wang, C. Molina, and E. Abdalla, Phys. Rev. D 63,084001 (2001).
[260]J. M. Zhu, B. Wang, and E. Abdalla, Phys. Rev. D 63,124004 (2001).
[261]V. Cardoso and J. P. S. Lemos, Phys. Rev. D 63,124015 (2001); 64,084017 (2001).
[262]E. Berti and K. D. Kokkotas, Phys. Rev. D 67,064020 (2003).
[263]L. Liu and B. Wang, Phys. Rev. D 78,064001 (2008).
[264]M. Maggiore, Phys. Rev. Lett.100,141301 (2008).
[265]S. W. Hawking and D. N. Page, Commun. Math. Phys.87,577 (1983).
[266]A. G. Riess et. al., Astronphys. J.116,1009 (1998).
[267]S. Perlmutter et. al., Astrophys. J.517,565 (1999).
[268]A. G. Riess et. al., Astrophys. J.560,49 (2001).
[269]S. Weinberg, Rev. Mod. Phys.61,1 (1989).
[270]R. R. Caldwell, R. Dave, and P. J. Steinhardt, Phys. Rev. Lett.80,1582 (1998).
[271]P. J. E. Peebles and A. Vilenkin, Phys. Rev. D 59,063505 (1999).
[272]P. J. Steinhardt, L. M. Wang, and I. Zlatev, Phys. Rev. D 59,123504 (1999).
[273]M. Doran and J. Jaeckel, Phys. Rev. D 66,043519 (2002).
[274]A. Y. Kamenshchik, U. Moschella, and V. Pasquier, Phys. Lett. B511,256 (2001).
[275]M. Li, Phys. Lett. B603,1 (2004); Q. G. Huang and M. Li, JCAP 08,013 (2004).
[276]R. R. Caldwell, Phys. Lett. B545,23 (2002).
[277]R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett.91, 071301 (2003).
[278]J. M. Cline, S. Y. Jeon, and G. D. Moore, Phys. Rev. D 70,043543 (2004).
[279]U. Alam, V. Sahni, and A. Starobinsky, JCAP 06,008 (2004).
[280]U. Alam, V. Sahni, T. Saini, and A. Starobinsky, Mon. Not. Roy. Astron. Soc.354, 275 (2004).
[281]R. Daly and S. Djorgovski, Astrophys. J.612,652 (2004).
[282]B. Wang, C. Y. Lin, and C. Molina, Phys. Rev. D 70,064025 (2004).
[283]Y. Wang and M. Tegmark, Phys. Rev. D 71,103513 (2005).
[284]Y. G. Gong, Class. Quant. Grav.22,2121 (2005).
[285]T. Choudhury and T. Padmanabhan, Astron. Astrophys.429,807 (2005).
[286]B. Feng, X. L.Wang, and X. M. Zhang, Phys. Lett. B607,35 (2005).
[287]W. Hu, Phys. Rev. D 71,047301 (2005).
[288]Z. K. Guo, Y. S. Piao, X. M. Zhang, and Y. Z. Zhang, Phys. Lett. B608,177 (2005).
[289]X. F. Zhang, H. Li, Y. S. Piao, and X. Zhang, Mod. Phys. Lett. A 21,231 (2006).
[290]M. Z. Li, B. Feng, and X. M. Zhang, JCAP 12,002 (2005).
[291]S. Nojiri and S. D. Odintsov, Phys. Lett. B562,147 (2003); Phys. Rev. D 70, 103522 (2004).
[292]S. Nojiri, S. D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71,063004 (2005).
[293]A. Vikman, Phys. Rev. D 71,023515 (2005).
[294]A. Anisimov, E. Babichev, and A. Vikman, JCAP 06,006 (2005).
[295]P. Singh, Class. Quant. Grav.22,4203 (2005).
[296]H. Stefancic, Phys. Rev. D 71,124036 (2005).
[297]B. Wang, Y. Gong, and E. Abdalla, Phys. Lett. B624,141 (2006).
[298]B. Wang, C. Y. Lin, and E. Abdalla, Phys. Lett. B637,357 (2006).
[299]B. Wang, J. D. Zang, C. Y. Lin, E. Abdalla and S. Micheletti, Nucl. Phys. B778, 69 (2007).
[300]E.O. Kahya and V. K. Onemli, Phys. Rev. D 76,043512 (2007).
[301]T. Koivisto and D. F. Mota, Phys. Lett. B644,104 (2007); Phys. Rev. D 75, 023518 (2007).
[302]G. R. Randall and R. Sundrum, Phys. Rev. Lett.83,3370 (1999); Phys. Rev. Lett. 83,4690 (1999).
[303]E. Kiritsis, N. Tetradis, and T. N. Tomaras, J. High Energy Phys.03,019 (2002).
[304]E. Kiritsis, G. Kofinas, N. Tetradis, T. N. Tomaras, and V. Zarikas, J. High Energy Phys.02,035 (2003).
[305]E. Kiritsis, JCAP 10,014 (2005).
[306]P. S. Apostolopoulos and N. Tetradis, Phys. Rev. D 71,043506 (2005); Phys. Lett. B633,409 (2006).
[307]K. I. Umezu et al., Phys. Rev. D 73,063527 (2006).
[308]R. G. Cai, Y. Gong, and B. Wang, JCAP 03,006 (2006).
[309]P. S. Apostolopoulos and N. Tetradis, Phys. Rev. D 74,064021 (2006).
[310]C. Bogdanos and K. Tamvakis, Phys. Lett. B646,39 (2007); C. Bogdanos, A. Dimitridis, and K. Tamvakis, Phys. Rev. D 75,087303 (2007).
[311]A. Sheykhi, B. Wang, and N. Riazi, Phys. Rev. D 75,123513 (2007).
[312]D. Lovelock, J. Math. Phys.12,498 (1971).
[313]B. Zwiebach, Phys. Lett. B156,315 (1985).
[314]D. G. Boulware and S. Deser, Phys. Rev. Lett.55,2656 (1985).
[315]G. Kofinas, R. Maartens, and E. Papantonopoulos, J. High Energy Phys.10,066 (2003).
[316]G. Dvali, G. Gabadadze, and M. Porrati, Phys. Lett. B485,208 (2000).
[317]G. Kofinas, G. Panotopoulos, and N. Tomaras, J. High Energy Phys.01,107 (2006).
[318]R. A. Brown, R. Maartens, E. Papantonopoulos, and V. Zamarias, JCAP 11,008 (2005).
[319]R. G. Cai, H. S. Zhang, and A. Wang, Commun. Theor. Phys.44,948 (2005).
[320]S. Yin, B. Wang, E. Abdalla, and C. Y. Lin, Phys. Rev. D 76,124026 (2007).
[321]C. Deffayet, Phys. Lett. B502,199 (2001).
[322]C. Barcelo, C. Germani, and C. F. Sopuerta, Phys. Rev. D 68,104007 (2003).
[323]R. Maartens, Phys. Rev. D 62,084023 (2000).
[324]D. N. Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl.148,175 (2003).
[325]E. V. Linder and A. Jenkins, Mon. Not. Roy. Astron. Soc.346,573 (2003).
[326]R. Jimenez, L. Verde, T. Treu, and D. Stern, Astrophys. J.593,622 (2003).
[327]J. Simon, L. Verde, and R. Jimenez, Phys. Rev. D 71,123001 (2005).
[328]W. L. Freedman, et al., Astrophys. J.553,47 (2001).
[329]J. H. He, B. Wang, and E. Papantonopoulos, Phys. Lett. B654,133, (2007).