暗能量及其相关问题的研究
摘要
近年来大量的天文观测表明宇宙正在加速膨胀。具有负压强的奇异物质暗能量成为了宇宙的主导成分。它均匀地分布在整个空间中,为宇宙的加速膨胀提供原动力。尽管人们对暗能量有了初步的认识,但是对它本质的了解却不多。暗能量已经成为了物理学研究中最重要的问题之一。
论文首先介绍了宇宙学的背景和标准宇宙学模型,然后对几种比较流行的暗能量模型做了简单介绍。
接着,主要研究有理想流体存在时标量场的动力学。由一个标量场来推动宇宙加速膨胀的动力学暗能量模型往往会遇到所谓的精细调节以及巧合性问题。为了解决这些问题,可以引入多组分的模型来求解标度解。在本文中,首先介绍标量场暗能量的自治系统,然后着重讨论了时空弯曲下有理想流体存在时快子暗能量的动力学,并求解标度解,通过对标度解的研究,确定它是稳定的还是短暂的。最后分别在开放宇宙和闭合宇宙两种可能的情况下探讨标度解的势具有什么样的形式及其演化。
另外,我们也研究和探讨暗能量的存在对行星进动角的影响。发现对于太阳系水星,暗能量对其进动角的贡献大约为总进动角的万分之一。因此,期望通过对水星进动的精密观测,可以推测暗能量的状态函数,并以此作为检验各种暗能量模型的理论依据。
最后是总结与展望,对整篇论文进行总结,并展望未来工作。
In recent years, numerous measurements all suggest that the universe is currently accelerating and is dominated by a component with negative pressure, which is named as dark energy. It permeates homogenously in all the universe and pushes the accelerated expansion of the universe. Although dark energy has been preliminarily known, its nature still remains mysterious. Dark energy has become one of the most important problems in the research frontier of physics and cosmology.
In this thesis, after briefly reviewing the background of cosmology and the standard cosmological model, we present some fashionable dark energy models.
After that, we investigate cosmological dynamics of scalar fields in the presence of a barotropic perfect fluid. The dynamical dark energy models driven by a scalar field suffer from the so called fine-tuning problem and coincidence problem, In order to address these problems, one may employ scalar field models exhibiting scaling solutions. Here we first explain the property of an autonomous system before entering the detailed analysis. Then we present the associated equations of motion for the tachyon field including the background fluid in spatially curved FRW universe and obtain the scaling solutions. Furthermore, by investigating the nature of scaling solutions, we determine whether such behavior is stable or just a transient feature. Then we turn to construct the scalar potential leading to such scaling solutions. In particular, its asymptotical forms are obtained in various circumstances for spatially open and closed universe respectively.
In chapter four, we are interested in the impact of dark energy on the perihelion shift of planets. For Mercury, we find an additional contribution due to dark energy, which is approximately 1/10000 of the total angular of the perihelion shift. Thus, it is possible to determine the equation of state of dark energy by observing the perihelion shift of Mercury. Furthermore, the conclusion may be helpful for checking up the dark energy models.
Chapter Fiver is both a conclusion and a prospect. It sums up the entire dissertation, and looks into the future work.
论文首先介绍了宇宙学的背景和标准宇宙学模型,然后对几种比较流行的暗能量模型做了简单介绍。
接着,主要研究有理想流体存在时标量场的动力学。由一个标量场来推动宇宙加速膨胀的动力学暗能量模型往往会遇到所谓的精细调节以及巧合性问题。为了解决这些问题,可以引入多组分的模型来求解标度解。在本文中,首先介绍标量场暗能量的自治系统,然后着重讨论了时空弯曲下有理想流体存在时快子暗能量的动力学,并求解标度解,通过对标度解的研究,确定它是稳定的还是短暂的。最后分别在开放宇宙和闭合宇宙两种可能的情况下探讨标度解的势具有什么样的形式及其演化。
另外,我们也研究和探讨暗能量的存在对行星进动角的影响。发现对于太阳系水星,暗能量对其进动角的贡献大约为总进动角的万分之一。因此,期望通过对水星进动的精密观测,可以推测暗能量的状态函数,并以此作为检验各种暗能量模型的理论依据。
最后是总结与展望,对整篇论文进行总结,并展望未来工作。
In recent years, numerous measurements all suggest that the universe is currently accelerating and is dominated by a component with negative pressure, which is named as dark energy. It permeates homogenously in all the universe and pushes the accelerated expansion of the universe. Although dark energy has been preliminarily known, its nature still remains mysterious. Dark energy has become one of the most important problems in the research frontier of physics and cosmology.
In this thesis, after briefly reviewing the background of cosmology and the standard cosmological model, we present some fashionable dark energy models.
After that, we investigate cosmological dynamics of scalar fields in the presence of a barotropic perfect fluid. The dynamical dark energy models driven by a scalar field suffer from the so called fine-tuning problem and coincidence problem, In order to address these problems, one may employ scalar field models exhibiting scaling solutions. Here we first explain the property of an autonomous system before entering the detailed analysis. Then we present the associated equations of motion for the tachyon field including the background fluid in spatially curved FRW universe and obtain the scaling solutions. Furthermore, by investigating the nature of scaling solutions, we determine whether such behavior is stable or just a transient feature. Then we turn to construct the scalar potential leading to such scaling solutions. In particular, its asymptotical forms are obtained in various circumstances for spatially open and closed universe respectively.
In chapter four, we are interested in the impact of dark energy on the perihelion shift of planets. For Mercury, we find an additional contribution due to dark energy, which is approximately 1/10000 of the total angular of the perihelion shift. Thus, it is possible to determine the equation of state of dark energy by observing the perihelion shift of Mercury. Furthermore, the conclusion may be helpful for checking up the dark energy models.
Chapter Fiver is both a conclusion and a prospect. It sums up the entire dissertation, and looks into the future work.
引文
[1]BENNETT C L,et al.Astrophys.J.Suppl[J].2003,148:1.
[2]SPERGEL D N, et al.Astrophys.J.Suppl[J].2003,148:175.
[3]何香涛,观测宇宙学(第二版)[M],北京师范大学出版社,2007。
[4]A.H.Guth Phys.Rev.D 23,34 7(1981).
[5]G.Gamow, Phys. Rev.70,572(1946). R. A. Alpher, H. Bethe and G. Gamow, Phys. Rev.73,803 (1948). G. Gamow, Phys. Rev.74,505(1948).
[6]Dicke.R.H and peebles.p.J.E, GeneralRelativity[M], England, Cambridge: CambridgeUniversity,1979, P,504.
[7]A.Albrecht and P.J.Steinhardt, Phys.Rev.Lett.48,1220(1982).
[8]P.de Bernardis et al., Nature 404,955(2000) [astro-ph/0004404].
[9]梁灿彬,周彬,微分几何入门与广义相对论(上册,第二版)[M],科学出版社,2006。
[10]E.W.KolbandM. Turner, The Early Universe[J], Addison-Wesley(1990).
[11]T.Padmanabhan, Theoretical,Astrophysics,Cambridge University Press[J] (2000).
[12]R.R.Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett.91,071301 (2003)
[13]P.de Bernardis et al., Nature 404,955 (2000) [astro-ph/0004404].
[14]S.Hanany et al., Astrophys. J.545, L5 (2000) [astro-ph/0005123].
[15]C.L.Bennett et al. (2003) [astro-ph/0302207].
[16]E. Komatsu et al. [WMAP Collaboration] [J], [arXiv:astro-ph/0803.0547].
[17]E.W.Kolb and M.S.Turner,1993, The early Universe [J] (Redwood City, Calif:Addison-Wesley).
[18]郭宗宽,暴涨宇宙学与暗能量中若干问题的研究[D],2005。
[19]庞兆广,若干不同宇宙演化模型的研究[D],2005
[20]A.H.Guth, Phys.Rev.D23,347(1981).
[21]吴建聘,热非高斯性和NAQDE暗能量模型的研究[D],2009
[22]周双勇,动力学暗能量模型的研究[D],2008
[23]E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of dark energy[J], [hep-th/0603057].
[24]S. M. Carroll,living Rev. rel.4,1(2001)..
[25]S. Weinberg, Rev.Mod. Phys.61,1(1989).
[26]Lemaitre G. Proe. Natl. Aead. Sci.U.S.A.2012; Albert Einstein, Philosopher-Seientist,1934, P.437.
[27]邵颖,博士论文：暗能量的标量场模型,2007
[28]CALDWELL R R,et al.Phys.Rev.Lett[J].1998,80;1 582
[29]PEEBLES P J E.RATRA B.Astrophys.J[J].1988,325:L 17.
[30]C. Wetterich, Nucl. Phys. B 302,668(1988).
[31]B. Ratra and J. Peebles, Phys. Rev. D37,321(1988).
[32]T. Barreiro, E. J. Copeland and N. J. Nunes, Phys. Rev. D 61,127301(2000).
[33]V. Sahni and L. M. Wang, Phys. Rev. D62,103517(2000).
[34]A. Albrecht and C. Skordis, Phys. Rev. Lett.84,2076(1999).
[35]Sahni V,Dark Mattera nd Dark Energy.The Physics of the Early Universe[J], Editor Papantonopoulos E, Springer 2005,141-180, [arXiv:astr-oph/0403324].
[36]Ratra B, Peebels P J E, Cosmological Consequences of a Roling Homogeneous Scalar Field[J], Phys. Rev. D,1988,37(12):3406—342.
[37]Wetterich C, Cosmology and the Fate of Dilatation Symmetry[J], Nuclear Physics B 1988, 302(4):668-696.
[38]S. M. Carroll, Phys. Rev. Lett.81,3067 (1998).
[39]A. Mazumdar, S. Panda and A. Perez-Lorenzana, Nucl. Phys. B 614,101 (2001). M. Fairbairn and M. H. G. Tytgat, Phys. Lett. B 546,1(2002). A. Feinstein, Phys. Rev. D 66,063511(2002). M. Sami, P. Chingangbam and T. Qureshi, Phys. Rev. D 66,043530 (2002). M. Sami, Mod. Phys. Lett. A 18,691 (2003). Y. S. Piao, R. G. Cai, X. m. Zhang and Y. Z. Zhang, Phys. Rev. D 66,121301 (2002).
[40]L. Kofman and A. Linde, JHEP 0207,004 (2002).
[41]T. Padmanabhan, Phys. Rev. D 66,021301(2002). J. S. Bagla, H. K. Jassal and T. Padmanabhan, Phys. Rev. D 67,063504 (2003). L. R. W. Abramo and F. Finelli, Phys. Lett. B 575 165 (2003). J. M. Aguirregabiria and R. Lazkoz, Phys. Rev. D 69,123502 (2004). Z. K. Guo and Y. Z. Zhang, JCAP 0408,010 (2004). E. J. Copeland, M. R. Garousi, M. Sami and S. Tsujikawa, Phys. Rev. D 71,043003 (2005).
[42]Kutasov and V. Niarchos, Nucl. Phys. B 666,56 (2003).
[43]C. Armendaariz-Picon, T. Damour, and V. Mukhanov, Phys. Lett. B 458, (1999) 209. J. Garriga and V. Mukhanov, Phys. Lett. B 458,219 (1999).
[44]C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Phys. Rev. Lett.85,4438 (2000).
[45]C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Phys. Rev. D 63,103510 (2001).
[46]P. S. Corasaniti, M. Kunz, D. Parkinson, E. J. Copeland and B. A. Bassett. Phys. Rev. D 70, 083006 (2004).
[47]U. Alam, V. Sahni, T. D. Saini and A. A. Starobinsky, Mon. Not. Roy. Astron. Soc.354,275 (2004).
[48]R. R. Caldwell, Phys. Lett. B 545,23-29 (2002).
[49]P. Singh, M. Sami and N. Dadhich, Phys. Rev. D 68 023522(2003).
[50]S. M. Carroll, M. Hoffman and M. Trodden, Phys. Rev. D 68,023509 (2003).
[51]D. Huterer A. Cooray, Uncorelated Estimates of Dark Eergy Evolution[J], Phy. Rev. D 205, 71 (2):02 3506(5), [arXiv:astro-ph/0404062].
[52]A. G Riess et al. New Hubble Space Telescope Discoveries of Type la Supernovae at z≥1:Narrowing Constraints on the Early Behavior of Dark Energy[J],2006, [arXiv:astro-ph/061162].
[53]B. Feng, X. L. Wang, and X. M. Zhang, Dark Energy Constraints from the Cosmic Age and Supernova[J], Phys. Lett. B 2005,607,35 [arXiv:astro-ph/0404224].
[54]A. Kamenshchik, U. MoscheUa, V. Pasquier, An Alternative to Quintessence, Phys. Lett. B51 1.2001.265.268
[55]K. Freesc, M. Lewis, Cardassian Expansion:a Model in which the UIIiveris Flat[J]. Matter Dominated, and Accelerating, Phys. Lett, B540,2002.1.8
[56]N. Bilic, G. B. Tupper, R. D. Viollier, Unification ofDark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas[J]. Phys. Lett. B535.2002.17.21
[57]Z. H. Zhu, Generalized Chaplygin Gas as a Unified Scenario of Dark Matter / Energy: Observational Constraints[J], Astron. Astrophys.423,2004.421-426
[58]M. C. Bento, O. Bertolami, The Revival of the Unified Dark Energy-Dark Matter Model[J], Phys. Rev. D70,2004.083519
[59]H. B. Benaoum, Accelerated Universe from Modified Chaplygin Gas and Tachyonic Fluid[J], arXiv: hep-th/0205140,2002
[60]L. P. Chimento, Extended Tachyon Field, Chaplygin Gas and Solvable K—essence Cosmologie[J]s, Phys. Rev. D69,2004.123517
[61]L. P. Chimento, R. Lazkoz, Large-scale Inhomogeneities in Modified Chaplygin Gas Cosmologies[J], Phys. Lett. B615,2005.146-152
[62]Z. K. Guo, Y. Z. Zhang, Cosmology with a Variable Chaplygin Gas[J], Phys. Lett. B645, 2007.326-329
[63]M. Li, A Model of Holographic Dark Energy[J], Phys.Lett. B603 (2004) 1, [arXiv:hep-th/0403127].
[64]X. Zhang, Reconstructing holographic quintessence[J], Phys. Lett. B 648 (2007) 1-7,[arXiv:astro-ph/0604484].
[65]Q. G. Huang, M.Li, the holographic dark energy in a non-flat universe[J], JCAP 0408 (2004) 013, [arXiv:astro-ph/0404229].
[66]J. Ellis, S. Kalara, K. A. Olive and C. Wetterich, Phys. Lett. B 1989,228,264
[67]Amendola L, Coupled Quintessence[J], Phys. Rev. D 2000,62(4):043511(10)..
[68]M. Szydlowski, Phys. Lett. B 2006,632,1.
[69]M.Szydlowski, T. Stachowisk and R. Wojtak, Phys. Rev. D 2006,73,06351.
[70]C. Wetterich, A and A 1995,301,321.
[71]T. Damour and A. M. Polyakov, Nucl. Phys. B 1994,423,532.
[72]G. W. Gibbons, Phys. Lett. B 537,1(2002).[arXiv:hep-th/0204008].
[73]F. Piazza and S. Tsujikawa, JCAP 0407 (2004) 004 [arXiv:hep-th/0405054].
[74]E. J. Copeland, M. R. Garousi, M. Sami and S. Tsujikawa, Phys. Rev. D71(2005) 043003[arXiv:hep-th/0411192].
[75]B. Gumjudpai, T. Naskar and J. Ward, JCAP 0611 (2006) 006 [arXiv:hep-ph/0603210].
[76]S. Tsujikawa, Phys. Rev. D 73 (2006) 103504 [arXiv:hep-th/0601178].
[77]Y. Gong, A. Wang and Y. Z. Zhang, Phys. Lett. B 636 (2006) 286 [arXiv:gr-qc/0603050].
[78]J. Martin and M. Yamaguchi, Phys. Rev. D 77 (2008) 123508 [arXiv:0801.3375v1].
[79]A. A. Sen and N. C. Devi, Phys. Lett. B 668,182 (2008) [arXiv:0804.2775v2].
[80]B. Gumjudpai and J. Ward,[arXiv:0904.0472v1].
[81]G. Calcagni, A.R. Liddle,Phys.Rev. D74 (2006) 043528[arXiv:astro-ph/0606003].
[82]P. G. Ferreira and M. Joyce, Phys.Rev. D58 (1998) 023503 [arXiv:astro-ph/9711102v3].
[83]E. J. Copeland, A. R. Liddle and D. Wands, Phys. Rev. D 57,4686 (1998) [arXiv:gr-qc/9711068].
[84]A. P. Billyard, A. A. Coley and R. J. van den Hoogen, Phys.Rev. D58 (1998) 123501 [arXiv:gr-qc/9805085].
[85]A. R. Liddle and R. J. Scherrer, Phys.Rev. D59 (1998) 023509 [arXiv:astro-ph/9809272].
[86]J. P. Uzan, Phys. Phys.Rev.D59 (1999) 123510 [arXiv:gr-qc/9903004].
[87]R. J.van den Hoogen, A. A. Coley and D. Wands, Class.Quantum.Grav.16:1843-1851,1999 [arXiv:gr-qc/9901014]
[88]A. Nunes and J. P. Mimoso, Phys. Lett. B 488,423(2000).
[89]A. de la Macorra and G. Piccinelli, Phys.Rev. D61 (2000) 123503 [arXiv:hep-ph/9909459].
[90]S. C. C. Ng, N. J. Nunes and F. Rosati, Phys.Rev.D64:083510,2001 [arXiv:astro-ph/0107321].
[91]C. Rubano and J. D. Barrow, Phys.Rev. D64 (2001) 127301 [arXiv:gr-qc/0105037]
[92]Z. K. Guo, Y. S. Piao, R. G. Cai and Y. Z. Zhang, Phys.Lett. B 576,12 (2003).
[93]Z. K. Guo, Y. S. Piao and Y. Z. Zhang, Phys.Lett. B 568,1 (2003).
[94]S. Mizuno, S. J. Lee and E. J. Copeland, Phys.Rev. D70 (2004) 043525 [arXiv:astro-ph/0405490].
[95]E. J. Copeland, S. J. Lee, J. E.Lidsey and S. Mizuno, Phys.Rev. D71 (2005) 023526 [arXiv:astro-ph/0410110].
[96]M. Sami, N.Savchenko and A. Toporensky, Phys.Rev. D64 (2001) 123526 [arXiv:hep-ph/0104186].
[97]V. Pettorino, C. Baccigalupi and F. Perrotta, JCAP 0512 (2005) 003 [arXiv:astro-ph/0508586].
[98]L.Amendola, S.Tsujikawa and M.Sami, Phys.Lett. B632 (2006) 155-158 [arXiv:astro-ph/0506222].
[99]S. Tsujikawa and M. Sami,Phys.Lett.B603:113-123,2004 [arXiv.hep-th/0409212]
[100]L. Amendola, M. Quartin, S. Tsujikawa and I. Waga, Phys.Rev. D74 (2006) 023525 [arXiv:astro-ph/0605488].
[101]S. Tsujikawa, M. Sami, JCAP0701:006,2007 [arXiv:hep-th/0608178v2]
[102]A. A. Coley and R. J. van den Hoogen, Phys. Rev. D 62,023517 (2000).
[103]S.A. Kim, A. R. Liddle and S. Tsujikawa, Phys. Rev. D 72,043506 (2005).
[104]E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl.180,330 (2009) [arXiv:0803.0547v2].
[105]E.J.Copeland, S.Mizuno, M.Shaeri, Phys. Rev. D 79,103515 (2009) [arXiv:0904.0877v2].
[106]B. Gumjudpai, T. Naskar, M. Sami, S. Tsujikawa, JCAP 0506:007,2005 [arXiv:hep-th/0502191].
[107]V. V. Kiselev. Quintessence and black holes [J]. Class. Quant. Grav.,2003,20:1187-1198.
[108]俞允强,广义相对论引论[M],北京大学出版社,1985。
[109]Moshe Carmeli and Tanya Kuzmenko. Value of the Cosmological Constant in the Cosmological Relativity Theory[J], International Journal of Theoretical Physics, 2002,Volume 41,
[110]Daris Samart and Burin Gumjudpai. Phantom field dynamics in loop quantum cosmology [J]. Phys. Rev. D,2007,76,043514,.
[2]SPERGEL D N, et al.Astrophys.J.Suppl[J].2003,148:175.
[3]何香涛,观测宇宙学(第二版)[M],北京师范大学出版社,2007。
[4]A.H.Guth Phys.Rev.D 23,34 7(1981).
[5]G.Gamow, Phys. Rev.70,572(1946). R. A. Alpher, H. Bethe and G. Gamow, Phys. Rev.73,803 (1948). G. Gamow, Phys. Rev.74,505(1948).
[6]Dicke.R.H and peebles.p.J.E, GeneralRelativity[M], England, Cambridge: CambridgeUniversity,1979, P,504.
[7]A.Albrecht and P.J.Steinhardt, Phys.Rev.Lett.48,1220(1982).
[8]P.de Bernardis et al., Nature 404,955(2000) [astro-ph/0004404].
[9]梁灿彬,周彬,微分几何入门与广义相对论(上册,第二版)[M],科学出版社,2006。
[10]E.W.KolbandM. Turner, The Early Universe[J], Addison-Wesley(1990).
[11]T.Padmanabhan, Theoretical,Astrophysics,Cambridge University Press[J] (2000).
[12]R.R.Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett.91,071301 (2003)
[13]P.de Bernardis et al., Nature 404,955 (2000) [astro-ph/0004404].
[14]S.Hanany et al., Astrophys. J.545, L5 (2000) [astro-ph/0005123].
[15]C.L.Bennett et al. (2003) [astro-ph/0302207].
[16]E. Komatsu et al. [WMAP Collaboration] [J], [arXiv:astro-ph/0803.0547].
[17]E.W.Kolb and M.S.Turner,1993, The early Universe [J] (Redwood City, Calif:Addison-Wesley).
[18]郭宗宽,暴涨宇宙学与暗能量中若干问题的研究[D],2005。
[19]庞兆广,若干不同宇宙演化模型的研究[D],2005
[20]A.H.Guth, Phys.Rev.D23,347(1981).
[21]吴建聘,热非高斯性和NAQDE暗能量模型的研究[D],2009
[22]周双勇,动力学暗能量模型的研究[D],2008
[23]E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of dark energy[J], [hep-th/0603057].
[24]S. M. Carroll,living Rev. rel.4,1(2001)..
[25]S. Weinberg, Rev.Mod. Phys.61,1(1989).
[26]Lemaitre G. Proe. Natl. Aead. Sci.U.S.A.2012; Albert Einstein, Philosopher-Seientist,1934, P.437.
[27]邵颖,博士论文：暗能量的标量场模型,2007
[28]CALDWELL R R,et al.Phys.Rev.Lett[J].1998,80;1 582
[29]PEEBLES P J E.RATRA B.Astrophys.J[J].1988,325:L 17.
[30]C. Wetterich, Nucl. Phys. B 302,668(1988).
[31]B. Ratra and J. Peebles, Phys. Rev. D37,321(1988).
[32]T. Barreiro, E. J. Copeland and N. J. Nunes, Phys. Rev. D 61,127301(2000).
[33]V. Sahni and L. M. Wang, Phys. Rev. D62,103517(2000).
[34]A. Albrecht and C. Skordis, Phys. Rev. Lett.84,2076(1999).
[35]Sahni V,Dark Mattera nd Dark Energy.The Physics of the Early Universe[J], Editor Papantonopoulos E, Springer 2005,141-180, [arXiv:astr-oph/0403324].
[36]Ratra B, Peebels P J E, Cosmological Consequences of a Roling Homogeneous Scalar Field[J], Phys. Rev. D,1988,37(12):3406—342.
[37]Wetterich C, Cosmology and the Fate of Dilatation Symmetry[J], Nuclear Physics B 1988, 302(4):668-696.
[38]S. M. Carroll, Phys. Rev. Lett.81,3067 (1998).
[39]A. Mazumdar, S. Panda and A. Perez-Lorenzana, Nucl. Phys. B 614,101 (2001). M. Fairbairn and M. H. G. Tytgat, Phys. Lett. B 546,1(2002). A. Feinstein, Phys. Rev. D 66,063511(2002). M. Sami, P. Chingangbam and T. Qureshi, Phys. Rev. D 66,043530 (2002). M. Sami, Mod. Phys. Lett. A 18,691 (2003). Y. S. Piao, R. G. Cai, X. m. Zhang and Y. Z. Zhang, Phys. Rev. D 66,121301 (2002).
[40]L. Kofman and A. Linde, JHEP 0207,004 (2002).
[41]T. Padmanabhan, Phys. Rev. D 66,021301(2002). J. S. Bagla, H. K. Jassal and T. Padmanabhan, Phys. Rev. D 67,063504 (2003). L. R. W. Abramo and F. Finelli, Phys. Lett. B 575 165 (2003). J. M. Aguirregabiria and R. Lazkoz, Phys. Rev. D 69,123502 (2004). Z. K. Guo and Y. Z. Zhang, JCAP 0408,010 (2004). E. J. Copeland, M. R. Garousi, M. Sami and S. Tsujikawa, Phys. Rev. D 71,043003 (2005).
[42]Kutasov and V. Niarchos, Nucl. Phys. B 666,56 (2003).
[43]C. Armendaariz-Picon, T. Damour, and V. Mukhanov, Phys. Lett. B 458, (1999) 209. J. Garriga and V. Mukhanov, Phys. Lett. B 458,219 (1999).
[44]C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Phys. Rev. Lett.85,4438 (2000).
[45]C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Phys. Rev. D 63,103510 (2001).
[46]P. S. Corasaniti, M. Kunz, D. Parkinson, E. J. Copeland and B. A. Bassett. Phys. Rev. D 70, 083006 (2004).
[47]U. Alam, V. Sahni, T. D. Saini and A. A. Starobinsky, Mon. Not. Roy. Astron. Soc.354,275 (2004).
[48]R. R. Caldwell, Phys. Lett. B 545,23-29 (2002).
[49]P. Singh, M. Sami and N. Dadhich, Phys. Rev. D 68 023522(2003).
[50]S. M. Carroll, M. Hoffman and M. Trodden, Phys. Rev. D 68,023509 (2003).
[51]D. Huterer A. Cooray, Uncorelated Estimates of Dark Eergy Evolution[J], Phy. Rev. D 205, 71 (2):02 3506(5), [arXiv:astro-ph/0404062].
[52]A. G Riess et al. New Hubble Space Telescope Discoveries of Type la Supernovae at z≥1:Narrowing Constraints on the Early Behavior of Dark Energy[J],2006, [arXiv:astro-ph/061162].
[53]B. Feng, X. L. Wang, and X. M. Zhang, Dark Energy Constraints from the Cosmic Age and Supernova[J], Phys. Lett. B 2005,607,35 [arXiv:astro-ph/0404224].
[54]A. Kamenshchik, U. MoscheUa, V. Pasquier, An Alternative to Quintessence, Phys. Lett. B51 1.2001.265.268
[55]K. Freesc, M. Lewis, Cardassian Expansion:a Model in which the UIIiveris Flat[J]. Matter Dominated, and Accelerating, Phys. Lett, B540,2002.1.8
[56]N. Bilic, G. B. Tupper, R. D. Viollier, Unification ofDark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas[J]. Phys. Lett. B535.2002.17.21
[57]Z. H. Zhu, Generalized Chaplygin Gas as a Unified Scenario of Dark Matter / Energy: Observational Constraints[J], Astron. Astrophys.423,2004.421-426
[58]M. C. Bento, O. Bertolami, The Revival of the Unified Dark Energy-Dark Matter Model[J], Phys. Rev. D70,2004.083519
[59]H. B. Benaoum, Accelerated Universe from Modified Chaplygin Gas and Tachyonic Fluid[J], arXiv: hep-th/0205140,2002
[60]L. P. Chimento, Extended Tachyon Field, Chaplygin Gas and Solvable K—essence Cosmologie[J]s, Phys. Rev. D69,2004.123517
[61]L. P. Chimento, R. Lazkoz, Large-scale Inhomogeneities in Modified Chaplygin Gas Cosmologies[J], Phys. Lett. B615,2005.146-152
[62]Z. K. Guo, Y. Z. Zhang, Cosmology with a Variable Chaplygin Gas[J], Phys. Lett. B645, 2007.326-329
[63]M. Li, A Model of Holographic Dark Energy[J], Phys.Lett. B603 (2004) 1, [arXiv:hep-th/0403127].
[64]X. Zhang, Reconstructing holographic quintessence[J], Phys. Lett. B 648 (2007) 1-7,[arXiv:astro-ph/0604484].
[65]Q. G. Huang, M.Li, the holographic dark energy in a non-flat universe[J], JCAP 0408 (2004) 013, [arXiv:astro-ph/0404229].
[66]J. Ellis, S. Kalara, K. A. Olive and C. Wetterich, Phys. Lett. B 1989,228,264
[67]Amendola L, Coupled Quintessence[J], Phys. Rev. D 2000,62(4):043511(10)..
[68]M. Szydlowski, Phys. Lett. B 2006,632,1.
[69]M.Szydlowski, T. Stachowisk and R. Wojtak, Phys. Rev. D 2006,73,06351.
[70]C. Wetterich, A and A 1995,301,321.
[71]T. Damour and A. M. Polyakov, Nucl. Phys. B 1994,423,532.
[72]G. W. Gibbons, Phys. Lett. B 537,1(2002).[arXiv:hep-th/0204008].
[73]F. Piazza and S. Tsujikawa, JCAP 0407 (2004) 004 [arXiv:hep-th/0405054].
[74]E. J. Copeland, M. R. Garousi, M. Sami and S. Tsujikawa, Phys. Rev. D71(2005) 043003[arXiv:hep-th/0411192].
[75]B. Gumjudpai, T. Naskar and J. Ward, JCAP 0611 (2006) 006 [arXiv:hep-ph/0603210].
[76]S. Tsujikawa, Phys. Rev. D 73 (2006) 103504 [arXiv:hep-th/0601178].
[77]Y. Gong, A. Wang and Y. Z. Zhang, Phys. Lett. B 636 (2006) 286 [arXiv:gr-qc/0603050].
[78]J. Martin and M. Yamaguchi, Phys. Rev. D 77 (2008) 123508 [arXiv:0801.3375v1].
[79]A. A. Sen and N. C. Devi, Phys. Lett. B 668,182 (2008) [arXiv:0804.2775v2].
[80]B. Gumjudpai and J. Ward,[arXiv:0904.0472v1].
[81]G. Calcagni, A.R. Liddle,Phys.Rev. D74 (2006) 043528[arXiv:astro-ph/0606003].
[82]P. G. Ferreira and M. Joyce, Phys.Rev. D58 (1998) 023503 [arXiv:astro-ph/9711102v3].
[83]E. J. Copeland, A. R. Liddle and D. Wands, Phys. Rev. D 57,4686 (1998) [arXiv:gr-qc/9711068].
[84]A. P. Billyard, A. A. Coley and R. J. van den Hoogen, Phys.Rev. D58 (1998) 123501 [arXiv:gr-qc/9805085].
[85]A. R. Liddle and R. J. Scherrer, Phys.Rev. D59 (1998) 023509 [arXiv:astro-ph/9809272].
[86]J. P. Uzan, Phys. Phys.Rev.D59 (1999) 123510 [arXiv:gr-qc/9903004].
[87]R. J.van den Hoogen, A. A. Coley and D. Wands, Class.Quantum.Grav.16:1843-1851,1999 [arXiv:gr-qc/9901014]
[88]A. Nunes and J. P. Mimoso, Phys. Lett. B 488,423(2000).
[89]A. de la Macorra and G. Piccinelli, Phys.Rev. D61 (2000) 123503 [arXiv:hep-ph/9909459].
[90]S. C. C. Ng, N. J. Nunes and F. Rosati, Phys.Rev.D64:083510,2001 [arXiv:astro-ph/0107321].
[91]C. Rubano and J. D. Barrow, Phys.Rev. D64 (2001) 127301 [arXiv:gr-qc/0105037]
[92]Z. K. Guo, Y. S. Piao, R. G. Cai and Y. Z. Zhang, Phys.Lett. B 576,12 (2003).
[93]Z. K. Guo, Y. S. Piao and Y. Z. Zhang, Phys.Lett. B 568,1 (2003).
[94]S. Mizuno, S. J. Lee and E. J. Copeland, Phys.Rev. D70 (2004) 043525 [arXiv:astro-ph/0405490].
[95]E. J. Copeland, S. J. Lee, J. E.Lidsey and S. Mizuno, Phys.Rev. D71 (2005) 023526 [arXiv:astro-ph/0410110].
[96]M. Sami, N.Savchenko and A. Toporensky, Phys.Rev. D64 (2001) 123526 [arXiv:hep-ph/0104186].
[97]V. Pettorino, C. Baccigalupi and F. Perrotta, JCAP 0512 (2005) 003 [arXiv:astro-ph/0508586].
[98]L.Amendola, S.Tsujikawa and M.Sami, Phys.Lett. B632 (2006) 155-158 [arXiv:astro-ph/0506222].
[99]S. Tsujikawa and M. Sami,Phys.Lett.B603:113-123,2004 [arXiv.hep-th/0409212]
[100]L. Amendola, M. Quartin, S. Tsujikawa and I. Waga, Phys.Rev. D74 (2006) 023525 [arXiv:astro-ph/0605488].
[101]S. Tsujikawa, M. Sami, JCAP0701:006,2007 [arXiv:hep-th/0608178v2]
[102]A. A. Coley and R. J. van den Hoogen, Phys. Rev. D 62,023517 (2000).
[103]S.A. Kim, A. R. Liddle and S. Tsujikawa, Phys. Rev. D 72,043506 (2005).
[104]E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl.180,330 (2009) [arXiv:0803.0547v2].
[105]E.J.Copeland, S.Mizuno, M.Shaeri, Phys. Rev. D 79,103515 (2009) [arXiv:0904.0877v2].
[106]B. Gumjudpai, T. Naskar, M. Sami, S. Tsujikawa, JCAP 0506:007,2005 [arXiv:hep-th/0502191].
[107]V. V. Kiselev. Quintessence and black holes [J]. Class. Quant. Grav.,2003,20:1187-1198.
[108]俞允强,广义相对论引论[M],北京大学出版社,1985。
[109]Moshe Carmeli and Tanya Kuzmenko. Value of the Cosmological Constant in the Cosmological Relativity Theory[J], International Journal of Theoretical Physics, 2002,Volume 41,
[110]Daris Samart and Burin Gumjudpai. Phantom field dynamics in loop quantum cosmology [J]. Phys. Rev. D,2007,76,043514,.