宇宙学标度解与暗能量的Statefinder诊断
|
摘要
随着大量天文观测数据的发布，宇宙学的研究已经进入了精确的黄金阶段。尤其是近年来，Ia型超新星的观测结果表明了宇宙正在加速膨胀。星系团的大尺度分布和源于Wilkinson Microwave Anisotropy Probe(WMAP)的精确数据也支持了这一结论。WMAP的数据表明宇宙在空间上几乎是平坦的，即Ω_(total)=1.02±0.02。另外，星系团的大尺度结构分布的研究结果表明暗物质的存在，它在宇宙中所占比份大约为Ω_(CDM)=0.27±0.04。这些观测结果表明宇宙中存在一种具有负压强的奇异物质成分—暗能量，它所占的比例约为2／3 (Ω_(de)=0.67±0.06)。暗能量均匀地分布在整个空间中为宇宙的加速膨胀提供动力。到目前为止，物理学家们已经建立了各种模型用以解释或说明宇宙的加速膨胀以及暗能量，如宇宙学常数模型，慢滚的标量场quintessence，phantom，quintom，以及暗能量和暗物质的耦合模型等。
本论文共五章，分别在四维标准宇宙学模型以及五维反弹宇宙学模型中探讨暗能量问题。我们的主要工作是第三章至第五章。第一章介绍了标准宇宙学模型，以及天文观测对暗能量的支持，并且详细介绍了几种暗能量的标量场模型。
第二章介绍了五维反弹宇宙模型。在该模型中，宇宙嵌入在五维Ricci平坦时空中的一个超曲面上，从五维看，它是空的或者真空。但是，从四维的角度看，宇宙中则充满着从额外维诱导出来的物质，被称为诱导物质。
第三章在五维反弹模型中，利用自治系统得到五维宇宙学标度解。利用该标度解对五维反弹模型的分析结果表明，五维宇宙的膨胀规律与四维宇宙是相同的，这种膨胀规律与四维宇宙具体位于哪个五维超曲面上无关。
第四章利用statefinder参数对四维暗能量模型进行了诊断。人们认为宇宙学常数Λ是解释宇宙加速膨胀的最简单的方案，但它存在着精细调节和巧合性问题。人们提出了许多暗能量模型，用以解释宇宙的加速膨胀，以及解决或缓解宇宙学常数的精细调节和巧合性问题。本论文的主要内容就是利用statefinder参数{r，s}对这些暗能量模型加以区分和诊断。在四维标准宇宙学模型中，利用statefinder参数对具有追踪势的quintessence模型，势能为V(φ)=V_0exp(-λφ~2)的鬼场模型，以及鬼场和暗物质的相互作用模型进行分析。对于前两个宇宙学模型的分析结果表明：statefinder参数{r，s}在这两个模型中的存在范围不同，statefinder参数对的演化轨迹r(s)以及参数r和减速因子q的演化轨迹r(q)也不相同。在势能为V(φ)=V_0exp(-λφ~2)的鬼场模型中，宇宙演化后期的吸引子行为不仅可以用相图来描述，而且也可以从r(s)和r(q)的演化轨迹中体现。在鬼场和暗物质的相互作用模型中，利用statefinder参数对该模型的分析可以得到，当宇宙演化进入两个不同的标度解时期，鬼场和暗物质的相互作用在这两种情形下对宇宙演化具有不同影响。另外，本文对有相互作用与没有相互作用存在的情况进行了比较。
第五章在五维反弹模型中，重新确定了statefinder参数{r，s}以及减速因子q的表达式，利用自治系统，得出五维模型中quintessence暗能量和phantom暗能量的吸引子解；利用statefinder参数和减速因子对它们进行了分析，同时也研究了标量场势能V(φ)中的参数λ对宇宙演化的影响。
With the issue of abundant data from observation, the cosmology has entered a golden era. Especially, the recent measurements of type Ia Supernovae (SNe Ia) are the most direct evidence of the presence of accelerating expansion of the universe, which is also confirmed by the combination of results from the large-scale distribution of galaxies and the most precise data on the cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe (WMAP). The data from WMAP indicate that the universe is almost spatially flat, i. e.Ω_(total)=1.02±0.02. Furthermore, the studies on large-scale distribution of the galaxies imply the existence of cold dark matter which occupies about 23% of the total energy of the universe, i. e.Ω_(CDM)=0.27±0.04. These results strongly imply the existence of a dubbed component with negative pressure, which is named as dark energy, and amounts to about 2/3 of the total energy of the universe (Ω_(de)=0.67±0.06). Dark energy permeates homogenously in all the universe and pushes the universe accelerating expansion. By far, many models have been presented to explain the accelerating expansion of the universe and dark energy, such as the cosmological constant A, slow rolling scalar fields quintessence, phantom, quintom and coupled models etc.
In this thesis, in the framework of the standard FRW cosmological model and the five-dimensional big bounce cosmological model, the accelerated expansion of the universe and the dark energy problem are explored. The dissertation includes five sections and our main contributions are given from Sec. 3 to Sec. 5. In Sec. 1, standard FRW cosmological model and the evidence of existence of dark energy from astronomical observation have been introduced. Meanwhile, several dark energy models are introduced also.
In Sec. 2, the five-dimensional big bounce cosmological model is introduced. In this model, the universe is a hypersurface embedded in a Ricci fiat five-dimensional manifold which is empty or vacuum from the higher dimensional view. However, from four-dimensional view, it is full of matter induced from the extra dimension, which is named as induced matter.
In Sec. 3, the scaling solution was obtained by the autonomous system in the five-dimensional cosmological model. The analysis of the phase-plane is shown that for this 5D scaling solution the universe expands with the same rate as it does in the 4D FRW models and not relies on which 4D hypersurface the universe is located in the 5D manifold.
In Sec. 4, several 4D dark energy models have been diagnosed by statefinder parameter {r, s}. It is supposed that the cosmological constant is the simplest model to explain the presence of the accelerating expansion of the universe. Unfortunately, there exist the fine-tuning and coincidence problems in cosmological constant model. However, many dark energy models have been presented to solve or alleviate the two problems. This thesis diagnoses various dark energy models with statefinder parameter {r, s}. In the 4D FRW cosmological model, the quintessence with tracker potential, the phantom model with V(Φ)= V_0 exp(-λΦ~2) and the coupled phantom energy with dark matter have been diagnosed by the statedfinder parameter. It is shown that the region of statefinder parameter, the trajectories of r(s) and r(q) are different between the former two models. Especially in attractor phantom model, attractor solution was studied by both phase-plane analysis and evolving trajectories of r(s) and r(q). In coupled phantom model, the two different scaling solutions have been studied by using statefinder parameter. It is found that the evolving trajectories of these two scaling solutions in the statefinder parameter plane are quite different. Meanwhile, the difference between the scenarios with and without the interaction has been contrasted.
In Sec. 5, in the five-dimensional big bounce model, the attractor solutions of quintessence and phantom field have been differentiated by statefinder parameter. It is found that the evolving trajectories of these two attractor solutions in the statefinder parameters plane are quite different, through which the effect on evolving of universe from the parameterλin potential also be studied.
本论文共五章，分别在四维标准宇宙学模型以及五维反弹宇宙学模型中探讨暗能量问题。我们的主要工作是第三章至第五章。第一章介绍了标准宇宙学模型，以及天文观测对暗能量的支持，并且详细介绍了几种暗能量的标量场模型。
第二章介绍了五维反弹宇宙模型。在该模型中，宇宙嵌入在五维Ricci平坦时空中的一个超曲面上，从五维看，它是空的或者真空。但是，从四维的角度看，宇宙中则充满着从额外维诱导出来的物质，被称为诱导物质。
第三章在五维反弹模型中，利用自治系统得到五维宇宙学标度解。利用该标度解对五维反弹模型的分析结果表明，五维宇宙的膨胀规律与四维宇宙是相同的，这种膨胀规律与四维宇宙具体位于哪个五维超曲面上无关。
第四章利用statefinder参数对四维暗能量模型进行了诊断。人们认为宇宙学常数Λ是解释宇宙加速膨胀的最简单的方案，但它存在着精细调节和巧合性问题。人们提出了许多暗能量模型，用以解释宇宙的加速膨胀，以及解决或缓解宇宙学常数的精细调节和巧合性问题。本论文的主要内容就是利用statefinder参数{r，s}对这些暗能量模型加以区分和诊断。在四维标准宇宙学模型中，利用statefinder参数对具有追踪势的quintessence模型，势能为V(φ)=V_0exp(-λφ~2)的鬼场模型，以及鬼场和暗物质的相互作用模型进行分析。对于前两个宇宙学模型的分析结果表明：statefinder参数{r，s}在这两个模型中的存在范围不同，statefinder参数对的演化轨迹r(s)以及参数r和减速因子q的演化轨迹r(q)也不相同。在势能为V(φ)=V_0exp(-λφ~2)的鬼场模型中，宇宙演化后期的吸引子行为不仅可以用相图来描述，而且也可以从r(s)和r(q)的演化轨迹中体现。在鬼场和暗物质的相互作用模型中，利用statefinder参数对该模型的分析可以得到，当宇宙演化进入两个不同的标度解时期，鬼场和暗物质的相互作用在这两种情形下对宇宙演化具有不同影响。另外，本文对有相互作用与没有相互作用存在的情况进行了比较。
第五章在五维反弹模型中，重新确定了statefinder参数{r，s}以及减速因子q的表达式，利用自治系统，得出五维模型中quintessence暗能量和phantom暗能量的吸引子解；利用statefinder参数和减速因子对它们进行了分析，同时也研究了标量场势能V(φ)中的参数λ对宇宙演化的影响。
With the issue of abundant data from observation, the cosmology has entered a golden era. Especially, the recent measurements of type Ia Supernovae (SNe Ia) are the most direct evidence of the presence of accelerating expansion of the universe, which is also confirmed by the combination of results from the large-scale distribution of galaxies and the most precise data on the cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe (WMAP). The data from WMAP indicate that the universe is almost spatially flat, i. e.Ω_(total)=1.02±0.02. Furthermore, the studies on large-scale distribution of the galaxies imply the existence of cold dark matter which occupies about 23% of the total energy of the universe, i. e.Ω_(CDM)=0.27±0.04. These results strongly imply the existence of a dubbed component with negative pressure, which is named as dark energy, and amounts to about 2/3 of the total energy of the universe (Ω_(de)=0.67±0.06). Dark energy permeates homogenously in all the universe and pushes the universe accelerating expansion. By far, many models have been presented to explain the accelerating expansion of the universe and dark energy, such as the cosmological constant A, slow rolling scalar fields quintessence, phantom, quintom and coupled models etc.
In this thesis, in the framework of the standard FRW cosmological model and the five-dimensional big bounce cosmological model, the accelerated expansion of the universe and the dark energy problem are explored. The dissertation includes five sections and our main contributions are given from Sec. 3 to Sec. 5. In Sec. 1, standard FRW cosmological model and the evidence of existence of dark energy from astronomical observation have been introduced. Meanwhile, several dark energy models are introduced also.
In Sec. 2, the five-dimensional big bounce cosmological model is introduced. In this model, the universe is a hypersurface embedded in a Ricci fiat five-dimensional manifold which is empty or vacuum from the higher dimensional view. However, from four-dimensional view, it is full of matter induced from the extra dimension, which is named as induced matter.
In Sec. 3, the scaling solution was obtained by the autonomous system in the five-dimensional cosmological model. The analysis of the phase-plane is shown that for this 5D scaling solution the universe expands with the same rate as it does in the 4D FRW models and not relies on which 4D hypersurface the universe is located in the 5D manifold.
In Sec. 4, several 4D dark energy models have been diagnosed by statefinder parameter {r, s}. It is supposed that the cosmological constant is the simplest model to explain the presence of the accelerating expansion of the universe. Unfortunately, there exist the fine-tuning and coincidence problems in cosmological constant model. However, many dark energy models have been presented to solve or alleviate the two problems. This thesis diagnoses various dark energy models with statefinder parameter {r, s}. In the 4D FRW cosmological model, the quintessence with tracker potential, the phantom model with V(Φ)= V_0 exp(-λΦ~2) and the coupled phantom energy with dark matter have been diagnosed by the statedfinder parameter. It is shown that the region of statefinder parameter, the trajectories of r(s) and r(q) are different between the former two models. Especially in attractor phantom model, attractor solution was studied by both phase-plane analysis and evolving trajectories of r(s) and r(q). In coupled phantom model, the two different scaling solutions have been studied by using statefinder parameter. It is found that the evolving trajectories of these two scaling solutions in the statefinder parameter plane are quite different. Meanwhile, the difference between the scenarios with and without the interaction has been contrasted.
In Sec. 5, in the five-dimensional big bounce model, the attractor solutions of quintessence and phantom field have been differentiated by statefinder parameter. It is found that the evolving trajectories of these two attractor solutions in the statefinder parameters plane are quite different, through which the effect on evolving of universe from the parameterλin potential also be studied.
引文
[1] 俞允强．《广义相对论引论》．北京：北京大学出版社，1997．
[2] 俞允强．《物理宇宙学讲义》．北京：北京大学出版社，2002．
[3] 梁灿彬．《微分几何与广义相对论》上、下．北京：北京师范大学出版社，2000．
[4] 须重明，吴雪君．《广义相对论与现代宇宙学》．南京：南京师范大学出版社，1999。
[5] Wald R M. General Relativity. Chicago: The University of Chicago Press, 1984.
[6] Liddle A R, Lyth D H. Cosmological inflation and large-scale structure. Cambridge University Press, 2000.
[7] Kinney W H. Cosmology, lnflation, and the Physics of Nothing. lectures given at the NATO advanced study institute on techniques and concepts of high energy physics, st. croix, USVI, 2002.
[8] Peebles P J E. The Cosmological Constant and Dark Energy. Rev. Mod. Phys. 2003, 75(2):559-606, astro-ph/0207347.
[9] Liddle A R. An Introduction to Cosmological Inflation. proceedings of ICIP summer school in highenergy physics, 1998.
[10] Weinberg S. Gravitation and cosmology: principles and applications of the general theory of relativity. New York, Wiley, 1972.
[11] Kolb E W, Turner M. The Early Universe. Redwood City, CA: Addison-Wesley, c1990.
[12] Padmanabhan T. Theoretical Astrophysics. Cambridge University Press, 2000.
[13] Spergel D N et al. First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. Astrophys. J. Suppl. 2003, 148(1):175-194, astro-ph/0302209.
[14] Turner M S. Dark Matter and Dark Energy in the Universe. in The Galactic Halo, Astronomical Society of the Pacific Conference Proceedings No. 165, edited by B. K. Gibson, Axelrod T S, and Putnam M E, Astron. Soc. Pac. Conf. Series 1999, 666, astro-ph/9811454.
[15] Baade W. The Absolute Photographic Magnitude of Supernovae. Astrophys. J. 1938, 88(1):285-305.
[16] Colgate S A. Supernovae as a standard candle for cosmology. Astrophys. J. 1979, 232(1):404-408.
[17] Branch D, Tammann G A. Type Ia Supernovae as Standard Candles. Ann. Rev. Astron. Astrophys. 1992, 30(9):359-389.
[18] Branch D. Type Ia Supernovae and the Hubble Constant. Ann. Rev. Astron. Astrophys. 1998, 36(9):17-55, astro-ph/9801065.
[19] Copeland Edmund J, Sami M, Tsujikawa Shinji. Dynamics of dark energy. Int. J. Mod. Phys. D 2006, 15(11): 1753-1936, hep-th/0603057.
[20] Perlmutter S. Measurements of Omega and Lambda from 42 High-Redshift Supernovae. Astrophys. J. 1999, 517(2):565-586, astro-ph/9812133.
[21] Riess A G, et al. [Supernova Search Team Collaboration]. Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. Astron. J. 1998, 116(3):1009-1038, astro-ph/9805201.
[22] Sahni V, Starobinsky A A. The Case for a Positive Cosmological Lambda-term. Int. J. Mod. Phys. D 2000, 9(04):373-443, astro-ph/9904398.
[23] Sahni V. Dark matter and dark energy. Lect. Notes Phys. 2004; 653:141-180, astro-ph/0403324.
[24] Padmanabhan T. Cosmological constant: The weight of the vacuum. Phys. Rept. 2003, 380(5- 6):235-320, hep-th/0212290.
[25] Padmanabhan T. Dark Energy: the Cosmological Challenge of the Millennium. Curr. Sci. 2005, 88(7): 1057-1067, astro-ph/0411044.
[26] Riess AG et al. [Supernova Search Team Collaboration]. Type Ia Supernova Discoveries at z > 1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution. Astrophys. J. 2004, 607(2):665 - 687, astro-ph/0402512.
[27] Choudhury T R, Padmanabhan T. Cosmological parameters from supernova observations: A critical comparison of three data sets. Astron. Astrophys. 2005, 429(3):807-818, astro-ph/0311622.
[28] Riess A G et al. [Supernova Search Team Collaboration]. New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy. Astrophys. J. 2007, 656, for March 10, astro-ph/0611572.
[29] Tegmark M et al. [SDSS Collaboration]. Cosmological parameters from SDSS and WMAP. Phys. Rev. D 2004, 69(10):103501(26), astro-ph/0310723.
[30] Seljak U et al.. Cosmological parameter analysis including SDSS Lyalpha forest and galaxy bias: Constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy. Phys. Rev. D 2005, 71(10):103515(20), astro-ph/0407372.
[31] Scott D, Smoot G. Cosmic Background Radiation Mini-Review . Phys. Lett. B 2004, 592(1-4):l-5, astro-ph/0406567.
[32] Page L et al.. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Interpretation of the TT and TE Angular Power Spectrum Peaks. Astrophys. J. Suppl. 2003, 148(1):233-241, astro-ph/0302220.
[33] Weinberg S. Curvature dependence of peaks in the cosmic microwave background distribution. Phys. Rev. D 2000, 62(12):127302(2), astro-ph/0006276.
[34] Sievers J L et al.. Cosmological Parameters from Cosmic Background Imager Observations and Comparisons with BOOMERANG, DASI, and MAXIMA. Astrophys. J. 2003, 591(2):599-622, astro- ph/0205387.
[35] Aldering G [SNAP Collaboration]. Overview of the SuperNova / Acceleration Probe (SNAP), Future Research Direction and Visions for Astronomy. Edited by Dressier, Alan M. Proceedings of the SPIE 2002, 4835(11):146-157, astro-ph/0209550.
[36] Crittenden R G, Turok N. Looking for A with the Rees-Sciama Effect. Phys. Rev. Lett. 1996, 76(4):575-578, astro-ph/9510072 .
[37] Rees M J, Sciama D W. Larger scale Density Inhomogeneities in the Universe. Nature 1968, 217(2):511-516.
[38] Weinberg S. The cosmological constant problem. Rev. Mod. Phys. 1989, 61(1):1-23.
[39] Arkani-Hamed N, Hall L J, Kolda C F et al. New Perspective on Cosmic Coincidence Problems. Phys. Rev. Lett. 2000, 85(21):4434-4437, astro-ph/0005111.
[40] Steinhardt P J. in Critical Problems in Physics, edited by Fitch V L and Marlow D R (Princeton University Press, Princeton, NJ, 1997).
[41] Copeland E J, Liddle A R, Wands D. Exponential potentials and cosmological scaling solutions. Phys. Rev. D 1998, 57(8):4686-4690, gr-qc/9711068.
[42] Barreiro T, Copeland E J, Nunes N J. Quintessence arising from exponential potentials. Phys. Rev. D 2000, 61(12):127301(4), astro-ph/9910214.
[43] Caldwell R R. A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state. Phys. Lett. B 2002, 545(1-2):23-29, astro-ph/9908168.
[44] Caldwell R R, Kamionkowski M, Weinberg N N. Phantom Energy: Dark Energy with ω < -1 Causes a Cosmic Doomsday. Phys. Rev. Lett. 2003, 91(7):071301(4), astro-ph/0302506.
[45] Carroll S M, Hoffman M, Trodden M. Can the dark energy equation-of-state parameter ω be less than -1. Phys. Rev. D 2003, 68(2):023509(11), astro-ph/0301273 .
[46] Parker L, Raval A. A new Look at the Accelerating Universe. Phys. Rev. Lett. 2001, 86(5):749-752.
[47] Johri V B. Phantom cosmologies. Phys. Rev. D 2004, 70(4):041303(5), astro-ph/0311293.
[48] Bento M C, Bertolami O, Sen A A. Revival of the unified dark energy-dark matter model? Phys. Rev. D 2004, 70(8):083519(7), astro-ph/0407239.
[49] Alam U, Salmi V. Supernovo Constraints on Branemorld Dark Energy, astro-ph/0209443.
[50] Salmi V, Shtanov Y. Brane world models of dark energy. JCAP 2003, 03(11):014, astro-ph/0202346.
[51] Singh P, Sami M, Dadhich N. Cosmological dynamics of a phantom field. Phys. Rev. D 2003, 68(2):023522(7), hep-th/0305110.
[52] Huterer D, Cooray A. Uncorrelated Estimates of Dark Energy Evolution. Phys. Rev. D 2005, 71(2):023506(5), astro-ph/0404062.
[53] Alam U, Sahni V, Starobinsky A A. The case for dynamical dark energy revisited. JCAP 2004, 04(06):008(16), astro-ph/0403687.
[54] Feng B, Wang X L, Zhang X M. Dark energy constraints from the cosmic age and supernova. Phys. Lett. B 2005, 607(1-2):35-41, astro-ph/0404224.
[55] Liddle A R, Scherrer R J. A classification of scalar field potentials with cosmological scaling solutions. Phys. Rev. D 1999, 59(2):023509(7), astro-ph/9809272.
[56] van den Hoogen R J, Coley A A, Wands D. Scaling Solutions in Robertson-Walker Spacetimes. Class. Quant. Grav. 1999, 16(6):1843-1851, gr-qc/9901014.
[57] de la Macorra A, Piccinelli G. Cosmological evolution of general scalar fields and quintessence. Phys. Rev. D 2000, 61(12), 123503(8), hep-ph/9909459.
[58] Nunes A, Mimoso J P. On the potentials yielding cosmological scaling solutions. Phys. Lett. B 2000, 488(3-4):423-427, gr-qc/0008003.
[59] Ng S C C, Nunes N J, Rosati F. Applications of scalar attractor solutions to cosmology. Phys. Rev. D 2001, 64(8):083510(9), astro-ph/0107321.
[60] Rubano C, Barrow J D. Scaling solutions and reconstruction of scalar field potentials. Phys. Rev. D 2001, 64(12):127301(7), gr-qc/0105037.
[61] Uzan J P. Cosmological scaling solutions of non-minimally coupled scalar fields. Phys. Rev. D 1999, 59(12):123510(10), gr-qc/9903004.
[62] Copland E J, Liddle A R, Lyth D H, et al. False vacuum inflation with Einstein gravity, Phys. Rev. D 1994, 49(12):6410-6433, astro-ph/9401011.
[63] Dine M, Randall L, Thomas S. Supersymmetry Breaking in the Early Universe. Phys. Rev. Lett. 1995, 75(3):398-401, hep-ph/9503303.
[64] Stewart E D. Inflation, supergravity, and superstrings. Phys. Rev. D 1995, 51(12):6847-6853, hep- ph/9405389.
[65] Percival I C, Richards D. Introduction to dynamics, Cambridge University Press (1983).
[66] Lucchin F, Matarrese S. Power-law inflation. Phys. Rev. D 1985, 32(6}:1316-1322.
[67] Kitada Y, Maeda K. Cosmic no-hair theorem in homogeneous spacetimes. I. Bianchi models. Class. Quantum. Grav. 1993, 10(4):703-734.
[68] Sahni V, Wang L. New Cosmological Model of Quintessence and Dark Matter. Phys. Rev. D 2000, 62(10):103517(4), astro-ph/9910097.
[69] Steinhardt P J, Wang L M, Zlatev I. Cosmological tracking solutions. Phys. Rev. D 1999, 59(12):123504(13), astro-ph/9812313.
[70] Ratra B, Peebels P J E. Cosmological Consequences of a Rolling Homogeneous Scalar Field. Phys. Rev. D 1988, 37(12):3406-3427.
[71] Wetterich C, Cosmology, the Fate of Dilatation Symmetry. Nuclear Physics B 1988, 302(4):668-696.
[72] Ferreira P G, Joyce M. Structure Formation with a Self-Tuning Scalar Field. Phys. Rev. Lett. 1997,79(24):4740 - 4743, astro-ph/9707286;
[73] Ferreira P G, Joyce M. Cosmology with a primordial scaling field. Phys. Rev. D 1998, 58(2):023503(23), astro-ph/9711102.
[74] Frieman J, Hill C T, Stebbins A, et al. Cosmology with Ultralight Pseudo Nambu-Goldstone Bosons. Phys. Rev. Lett. 1995, 75(11):2077-2080, astro-ph/9505060.
[75] Brax P, Martin J. Robustness of quintessence. Phys. Rev. D 2000, 61(10):103502(14), astro- ph/9912046.
[76] Sahni V, Starobinsky A A. The Case for a Positive Cosmological Lambda-term. Int. J. Mod. Phys. D 2000, 9(4):373-444, astro-ph/9904398.
[77] Urena-López, L A, Liddle A. Supermassive Black Holes in Scalar Field Galaxy Halos. Phys. Rev. D 2002, 66(8):083005(5), astro-ph/0207493.
[78] Barreiro T, Copeland E J, Nunes N J. Quintessence Arising from Exponential Potentials. Phys. Rev. D 2000, 61(12):127301(4), astro-ph/9910214.
[79] Zlatev I, Wang L, Steinhardt P J. Quintessence, Cosmic Coincidence, and the Cosmological Constant. Phys. Rev. Lett. 1999. 82(2):896-899, astro-ph/9807002.
[80] Albrecht A, Burgess C P, Ravndal F. et al. Natural Quintessence and Large Extra Dimensions. Phys. Rev. D 2002, 65(12):123507(10), astro-ph/0107573.
[81] Sami M, Toporensky A. Phantom Field and the Fate of Universe. Mod. Phys. Lett. A 2004, 19(20):1509-1517, gr-qc/0312009.
[82] Overduin J M. Wesson P S. Kaluza-Klein Gravity. Phys. Rept. 1997, 283(5-6):303-379.
[83] Wesson P S. Space-Time-Matter. Singapore: World Scientific, 1999.
[84] Sabbata de V, Schmutzer E. Unified Field Theories of More Than 4 Dimensions, proc. international school of cosmology and gravitation. Erice, World Scientific, Singapore, 1983.
[85] Lee H C. An Introduction to Kaluza-Klein Theories, proc. Chalk River workshop on Kaluza-Klein theories, Singapore: World Scientific, 1984.
[86] Kang K, Fried H, Frampton P. Fifth workshop on grand unification. Singapore: World Scientific, 1984.
[87] Piran T, Weinberg S. Physics in Higher Dimensions, proc. 2nd Jerusalem winter school of theoretical physics. Singapore: World Scientific, 1986.
[88] Appelquist T, Chodos A, Freund P G 0. Modern Kaluza-Klein Theories. Menlo Park: Addison- Wesley, 1987.
[89] Collins P D B, Martin A D, Squires E J. Particle Physics and Cosmology. New York: Wiley, 1989.
[90] Duff M J, Nilsson B E W, Pope C N. Kaluza-Klein Supergravity. Phys. Rep. 1986, 130(1)1-85.
[91] Bailin D, Love A. Kaluza-Klein Theories. Rep. Prog. Phys. 1987, 50(9):1087-1170.
[92] Duff M J. Kaluza-Klein Theory in Perspective, hep-th/9410046.
[93] Randall L, Sundrum R. An Alternative to Compactification. Phys. Rev. Lett. 1999, 83(23):4690(4), hep-th/9906064.
[94] Randall L, Sundrum R. Large Mass Hierarchy from a Small Extra Dimension. Phys. Rev. Lett. 1999, 83(17):3370(4), hep-ph/9905221.
[95] Kaluza T. Zum Unitatsproblem der Physik. Sitz. Preuss. Akad. Wiss. Phys. Math. 1921 Kl:966
[96] Klein O. Quantentheorie and funfdimensionale Relativitatstheorie. Zeits. Phys. 1926, 37: 859
[97] Bergmann P G. Unified Field Theory with Fifteen Field Variables. Ann. Math. 1948, 49(1):255-264.
[98] Lessner G. Unified field theory on the basis of the projective theory of relativity. Phys. Rev. D 1982, 25(12):3202-3217, gr-qc/0005079.
[99] Liu H Y, Wesson P S. The physical properties of charged five-dimensional black holes. Class. Quant. Grav. 1997, 14(7):1651-1654.
[100] Wesson P S. An Embedding for General Relativity with Variable Rest Mass. Gen. Rel. Grav. 1984, 16(2):193203.
[101] Liu H Y, Mashhoon B. Spacetime measurements in Kaluza-Klein gravity. Phys. Lett. A 2000, 272(1-2):26-31.
[102] Campbell J E. A Course of Differential Geometry. Clarendon: Oxford, 1926.
[103] Guth A H. Inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D 1981, 23(2):347-356.
[104] Linde A D. A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Phys. Lett. B 1982, 108(6):389-393.
[105] Linde A D. Chaotic inflation. Phys. Lett. B 1983, 129(3-4):177-181 .
[106] Coble K, Dodelson S, Frieman J A. Dynamical A models of structure formation. Phys. Rev. D 1997, 55(4):1851-1859, astro-ph/9608122.
[107] Caldwell R R, Steinhardt P J. Imprint of gravitational waves in models dominated by a. dynamical cosmic scalar field. Phys. Rev. D 1998, 57(10):6057-6064, astro-ph/9710062.
[108] Zlatev I, Wang L M, Steinhardt P J. Quintessence, Cosmic Coincidence, and the Cosmological Constant. Phys. Rev. Left. 1999, 82(5):896-899, astro-ph/9807002.
[109] Heard I P C, Wands D. Cosmology with positive and negative exponential potentials. Class. Quant. Grav. 2002, 19(21):5435-5447, gr-qc/0206085.
[110] Guo Z K, Piao Y S, Cai R G et al. Cosmological scaling solutions and cross-coupling exponential potential. Phys. Lett. B 2003, 576(1-2):12-17, hep-th/0306245.
[111] Gno Z K, Piao Y S, Zhang Y Z. Cosmological scaling solutions and multiple exponential potentials. Phys. Lett. B 2003, 568(1-2):1-7, hep-th/0304048.
[112] Liu H Y, Wesson P S. Universe Models with a Variable Cosmological "Constant" and a "Big Bounce". Astrophys. J. 2001, 562(i):1-12, gr-qc/0107093.
[113] Overduin J M, Wesson P S. Kaluza-Klein gravity. Phys. Rep. 1997, 283(5-6):303-378, grqc/9805018.
[114] Chang B R, Liu H Y, Xu L X. Five-Dimensional Cosmological Scaling Solution. Mod. Phys. Lett. A 2005, 20(12):923-928, astro-ph/0405084.
[115] Liu H Y, Mashhoon B. A Machian interpretation of the cosmological constant. Ann.de Physik 1995, 4:565-582.
[116] Liu H Y. Exact Global Solutions of Brane Universe and Big Bounce. Phys. Lett. B, 2003, 560(3-4):149-154, hep-th/0206198.
[117] Wang B L, Liu H Y, Xu L X. Accelerating Universe in a Big Bounce Model. Mod. Phys. Lett. A 2004, 19(6):449-456, gr-qc/0304093.
[118] Xu L X, Liu H Y, Wang B L. On the Big Bounce Singularity of a Simple 5D Cosmological Model. Chin. Phys. Left. 2003, 20(7):995-998, gr-qc/0304049.
[119] Sahni V, Saini T D. Starobinsky A A and Alam U, Statefinder—A new geometrical diagnostic of dark energy. JETP Lett. 2003, 77(5):201-206, astro-ph/0201498.
[120] 张鑫．宇宙学常数与暗能量的若干问题：(博士学位论文)．北京：中国科学院高能物理研究所，2006．
[121] Zimdahl W, Pavon D. Letter: Statefinder Parameters for Interacting Dark Energy. Gen. Rel. Gray. 2004, 36(6):1483-1491, gr-qc/0311067.
[122] Alam U, Sahni V, Saini T D et al. Exploring the expanding Universe and dark energy using the statefinder diagnostic. Mon. Not. Roy. Astron. Soc. 2003, 344(4):1057-1074, astro-ph/0303009.
[123] Gorini V, Kamenshchik A, Moschella U. Can the Chaplygin gas be a plausible model for dark energy? Phys. Rev. D 2003, 67(6):063509(5), astro-ph/0209395.
[124] Zhang X. Statefinder diagnostic for coupled quintessence. Phys. Lett. B 2005, 611(1-2):1-7, astro-ph/0503075.
[125] Zhang X. Statefinder Diagnostic for Holographic Dark Energy Model. Int. J. Mod. Phys. D 2005, 14(09):1597-1606, astro-ph/0504586.
[126] Wu P X, Yu H W. Statefinder Parameters for Quintom Dark Energy Model. Int. J. Mod. Phys. D 2005, 14(11):1873-1881, gr-qc/0509036.
[127] Zhang X, Wu F Q, Zhang J F. New generalized Chaplygin gas as a scheme for unification of dark energy and dark matter. JCAP 2006, 06(01):003, astro-ph/0411221.
[128] Setare M R, Zhang J F, Zhang X. Statefinder diagnosis in a non-flat universe and the holographic model of dark energy. JCAP 2007, 07(03):007, gr-qc/0611084.
[129] Zlatev I, Steinhardt P J. A tracker solution to the cold dark matter cosmic coincidence problem. Phys. Lett. B 1999, 459(4):570-574, astro-ph/9906481.
[130] Ratra B, Peebels P J E. Cosmological consequences of a roiling homogeneous scalar field. Phys. Rev. D 1988, 37(12):3406-3427.
[131] Chang B R, Liu H Y, Xu L X et al. Statefinder Parameters for Quintessence with Tracker Potential. submitted to Prog. Theor. Phys.
[132] Guo Z K, Zhang Y Z. Interacting phantom energy. Phys. Rev. D 2005, 71(2):023501(5), astro-ph/0411524.
[133] Guo Z K, Cai R G, Zhang Y Z. Cosmological evolution of interacting phantom energy with dark matter. JCAP 2005, 05(05):002, astro-ph/0412624.
[134] Liu H Y, Liu H Y, Chang B R et al. Induced Phantom and 5D Attractor Solution in SpacetimeMatter Theory. Mod. Phys. Lett. A 2005, 20(26):1973-1982, gr-qc/0504021.
[135] Chang B R, Liu H Y, Xu L X et al. Statefinder Diagnostic for Phantom Model with V(φ) = V_0 exp(-λφ~2). Chin. Phys. Lett 2007, 24(7):2153-2156, arXiv:0704.3768.
[136] Guo Z K, Piao Y S, Zhang X M et al. Cosmological evolution of a quintom model of dark energy. Phys. Lett. B 2005, 608(3-4):177-182, astro-ph/0410654.
[137] Hao J G, Li X Z. Phantom cosmic dynamics: Tracking attractor and cosmic doomsday. Phys. Rev. D 2004, 70:043529(7), astro-ph/0309746.
[138] Chang B R, Liu H Y, Xu LX et al. Statefinder parameters for interacting phantom energy with dark matter. JCAP 2007, 07(01):016, astro-ph/0612616.
[139] Liko T, Wesson P S. The Big Bang as a Phase Transition. Int. J. Mod. Phys. A 2005, 20(10):2037-2045, gr-qc/0310067;
[140] Xu L X, Liu H Y. Three Components Evolution in a Simple Big Bounce Cosmological Model. Int. J. Mod. Phys. D 2005, 14 (5):883-892, astro-ph/0412241.
[141] Xu L X, Liu H Y. Scaling Dark Energy in a Five-Dimensional Bouncing Cosmological Model. Int. J. Mod. Phys. D 2005, 14(11):1947-1957, astro-ph/0507250.
[142] Xu L X, Liu H Y, Chang B R. Correspondence Between 5D Ricci-Flat Cosmological Models and Quintessence Dark Energy Models. Mod. Phys. Lett. A. 2006, 21(40):3105-3114, astro-ph/0507397.
[143] Xu L X, Liu H Y, Zhang C W. Reconstruction of 5D Cosmological Models from the Equation of State of Dark Energy. Int. J. Mod. Phys. D 2006, 15(2):215-224, astro-ph/0510673.
[144] Xu L X, Liu H Y, Ping Y L. Reconstruction of Five-dimensional Bounce cosmological Models From Deceleration Factor. Int. J. Theor. Phys. 2006, 45(4):843-850, astro-ph/0601471.
[145] Zhang C W, Liu H Y, Xu L X et al. Universe Evolution in a 5D Ricci-Flat Cosmology. Mod. Phys. Lett. A 2006, 21(7): 571-580, astro-ph/0602414.
[146] Ping Y L, Liu H Y, Xu L X. Using (4+1) Split and Energy Conditions to Study the Induced Matter in 5D Ricci-Flat Cosmology. Int. J. Mod. Phys. A2 007, 22(5):985-994, gr-qc/0610094.
[147] Liu M L, Liu H Y, Xu L X et al. Radiation and Potential Barriers of a 5D Black String Solution. Mod. Phys. Lett. A 2006, 21(39):2937-2945, gr-qc/0611137.
[148] Chang B R, Liu H Y, Xu L X et al. Statefinder Parameters for Five-Dimensional Cosmology. To be published in Mod. Phys. Lett. A.
[149] Hao J G, Li X Z. Constructing dark energy models with a late time de Sitter attractor. Phys. Rev. D 2003, 68(8):083514(7), hep-th0306033;
[150] Guo Z K, Piao Y S, Zhang Y Z. Attractor behavior of phantom cosmology. Phys. Lett. B 2004, 594(3-4):247-251, astro-ph/0404225. Notation: astro-ph/, hep-th/, gr-qc/please see http://Arxiv.org/abs/xx-xx/xxxxxxx.
[2] 俞允强．《物理宇宙学讲义》．北京：北京大学出版社，2002．
[3] 梁灿彬．《微分几何与广义相对论》上、下．北京：北京师范大学出版社，2000．
[4] 须重明，吴雪君．《广义相对论与现代宇宙学》．南京：南京师范大学出版社，1999。
[5] Wald R M. General Relativity. Chicago: The University of Chicago Press, 1984.
[6] Liddle A R, Lyth D H. Cosmological inflation and large-scale structure. Cambridge University Press, 2000.
[7] Kinney W H. Cosmology, lnflation, and the Physics of Nothing. lectures given at the NATO advanced study institute on techniques and concepts of high energy physics, st. croix, USVI, 2002.
[8] Peebles P J E. The Cosmological Constant and Dark Energy. Rev. Mod. Phys. 2003, 75(2):559-606, astro-ph/0207347.
[9] Liddle A R. An Introduction to Cosmological Inflation. proceedings of ICIP summer school in highenergy physics, 1998.
[10] Weinberg S. Gravitation and cosmology: principles and applications of the general theory of relativity. New York, Wiley, 1972.
[11] Kolb E W, Turner M. The Early Universe. Redwood City, CA: Addison-Wesley, c1990.
[12] Padmanabhan T. Theoretical Astrophysics. Cambridge University Press, 2000.
[13] Spergel D N et al. First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. Astrophys. J. Suppl. 2003, 148(1):175-194, astro-ph/0302209.
[14] Turner M S. Dark Matter and Dark Energy in the Universe. in The Galactic Halo, Astronomical Society of the Pacific Conference Proceedings No. 165, edited by B. K. Gibson, Axelrod T S, and Putnam M E, Astron. Soc. Pac. Conf. Series 1999, 666, astro-ph/9811454.
[15] Baade W. The Absolute Photographic Magnitude of Supernovae. Astrophys. J. 1938, 88(1):285-305.
[16] Colgate S A. Supernovae as a standard candle for cosmology. Astrophys. J. 1979, 232(1):404-408.
[17] Branch D, Tammann G A. Type Ia Supernovae as Standard Candles. Ann. Rev. Astron. Astrophys. 1992, 30(9):359-389.
[18] Branch D. Type Ia Supernovae and the Hubble Constant. Ann. Rev. Astron. Astrophys. 1998, 36(9):17-55, astro-ph/9801065.
[19] Copeland Edmund J, Sami M, Tsujikawa Shinji. Dynamics of dark energy. Int. J. Mod. Phys. D 2006, 15(11): 1753-1936, hep-th/0603057.
[20] Perlmutter S. Measurements of Omega and Lambda from 42 High-Redshift Supernovae. Astrophys. J. 1999, 517(2):565-586, astro-ph/9812133.
[21] Riess A G, et al. [Supernova Search Team Collaboration]. Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. Astron. J. 1998, 116(3):1009-1038, astro-ph/9805201.
[22] Sahni V, Starobinsky A A. The Case for a Positive Cosmological Lambda-term. Int. J. Mod. Phys. D 2000, 9(04):373-443, astro-ph/9904398.
[23] Sahni V. Dark matter and dark energy. Lect. Notes Phys. 2004; 653:141-180, astro-ph/0403324.
[24] Padmanabhan T. Cosmological constant: The weight of the vacuum. Phys. Rept. 2003, 380(5- 6):235-320, hep-th/0212290.
[25] Padmanabhan T. Dark Energy: the Cosmological Challenge of the Millennium. Curr. Sci. 2005, 88(7): 1057-1067, astro-ph/0411044.
[26] Riess AG et al. [Supernova Search Team Collaboration]. Type Ia Supernova Discoveries at z > 1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution. Astrophys. J. 2004, 607(2):665 - 687, astro-ph/0402512.
[27] Choudhury T R, Padmanabhan T. Cosmological parameters from supernova observations: A critical comparison of three data sets. Astron. Astrophys. 2005, 429(3):807-818, astro-ph/0311622.
[28] Riess A G et al. [Supernova Search Team Collaboration]. New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy. Astrophys. J. 2007, 656, for March 10, astro-ph/0611572.
[29] Tegmark M et al. [SDSS Collaboration]. Cosmological parameters from SDSS and WMAP. Phys. Rev. D 2004, 69(10):103501(26), astro-ph/0310723.
[30] Seljak U et al.. Cosmological parameter analysis including SDSS Lyalpha forest and galaxy bias: Constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy. Phys. Rev. D 2005, 71(10):103515(20), astro-ph/0407372.
[31] Scott D, Smoot G. Cosmic Background Radiation Mini-Review . Phys. Lett. B 2004, 592(1-4):l-5, astro-ph/0406567.
[32] Page L et al.. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Interpretation of the TT and TE Angular Power Spectrum Peaks. Astrophys. J. Suppl. 2003, 148(1):233-241, astro-ph/0302220.
[33] Weinberg S. Curvature dependence of peaks in the cosmic microwave background distribution. Phys. Rev. D 2000, 62(12):127302(2), astro-ph/0006276.
[34] Sievers J L et al.. Cosmological Parameters from Cosmic Background Imager Observations and Comparisons with BOOMERANG, DASI, and MAXIMA. Astrophys. J. 2003, 591(2):599-622, astro- ph/0205387.
[35] Aldering G [SNAP Collaboration]. Overview of the SuperNova / Acceleration Probe (SNAP), Future Research Direction and Visions for Astronomy. Edited by Dressier, Alan M. Proceedings of the SPIE 2002, 4835(11):146-157, astro-ph/0209550.
[36] Crittenden R G, Turok N. Looking for A with the Rees-Sciama Effect. Phys. Rev. Lett. 1996, 76(4):575-578, astro-ph/9510072 .
[37] Rees M J, Sciama D W. Larger scale Density Inhomogeneities in the Universe. Nature 1968, 217(2):511-516.
[38] Weinberg S. The cosmological constant problem. Rev. Mod. Phys. 1989, 61(1):1-23.
[39] Arkani-Hamed N, Hall L J, Kolda C F et al. New Perspective on Cosmic Coincidence Problems. Phys. Rev. Lett. 2000, 85(21):4434-4437, astro-ph/0005111.
[40] Steinhardt P J. in Critical Problems in Physics, edited by Fitch V L and Marlow D R (Princeton University Press, Princeton, NJ, 1997).
[41] Copeland E J, Liddle A R, Wands D. Exponential potentials and cosmological scaling solutions. Phys. Rev. D 1998, 57(8):4686-4690, gr-qc/9711068.
[42] Barreiro T, Copeland E J, Nunes N J. Quintessence arising from exponential potentials. Phys. Rev. D 2000, 61(12):127301(4), astro-ph/9910214.
[43] Caldwell R R. A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state. Phys. Lett. B 2002, 545(1-2):23-29, astro-ph/9908168.
[44] Caldwell R R, Kamionkowski M, Weinberg N N. Phantom Energy: Dark Energy with ω < -1 Causes a Cosmic Doomsday. Phys. Rev. Lett. 2003, 91(7):071301(4), astro-ph/0302506.
[45] Carroll S M, Hoffman M, Trodden M. Can the dark energy equation-of-state parameter ω be less than -1. Phys. Rev. D 2003, 68(2):023509(11), astro-ph/0301273 .
[46] Parker L, Raval A. A new Look at the Accelerating Universe. Phys. Rev. Lett. 2001, 86(5):749-752.
[47] Johri V B. Phantom cosmologies. Phys. Rev. D 2004, 70(4):041303(5), astro-ph/0311293.
[48] Bento M C, Bertolami O, Sen A A. Revival of the unified dark energy-dark matter model? Phys. Rev. D 2004, 70(8):083519(7), astro-ph/0407239.
[49] Alam U, Salmi V. Supernovo Constraints on Branemorld Dark Energy, astro-ph/0209443.
[50] Salmi V, Shtanov Y. Brane world models of dark energy. JCAP 2003, 03(11):014, astro-ph/0202346.
[51] Singh P, Sami M, Dadhich N. Cosmological dynamics of a phantom field. Phys. Rev. D 2003, 68(2):023522(7), hep-th/0305110.
[52] Huterer D, Cooray A. Uncorrelated Estimates of Dark Energy Evolution. Phys. Rev. D 2005, 71(2):023506(5), astro-ph/0404062.
[53] Alam U, Sahni V, Starobinsky A A. The case for dynamical dark energy revisited. JCAP 2004, 04(06):008(16), astro-ph/0403687.
[54] Feng B, Wang X L, Zhang X M. Dark energy constraints from the cosmic age and supernova. Phys. Lett. B 2005, 607(1-2):35-41, astro-ph/0404224.
[55] Liddle A R, Scherrer R J. A classification of scalar field potentials with cosmological scaling solutions. Phys. Rev. D 1999, 59(2):023509(7), astro-ph/9809272.
[56] van den Hoogen R J, Coley A A, Wands D. Scaling Solutions in Robertson-Walker Spacetimes. Class. Quant. Grav. 1999, 16(6):1843-1851, gr-qc/9901014.
[57] de la Macorra A, Piccinelli G. Cosmological evolution of general scalar fields and quintessence. Phys. Rev. D 2000, 61(12), 123503(8), hep-ph/9909459.
[58] Nunes A, Mimoso J P. On the potentials yielding cosmological scaling solutions. Phys. Lett. B 2000, 488(3-4):423-427, gr-qc/0008003.
[59] Ng S C C, Nunes N J, Rosati F. Applications of scalar attractor solutions to cosmology. Phys. Rev. D 2001, 64(8):083510(9), astro-ph/0107321.
[60] Rubano C, Barrow J D. Scaling solutions and reconstruction of scalar field potentials. Phys. Rev. D 2001, 64(12):127301(7), gr-qc/0105037.
[61] Uzan J P. Cosmological scaling solutions of non-minimally coupled scalar fields. Phys. Rev. D 1999, 59(12):123510(10), gr-qc/9903004.
[62] Copland E J, Liddle A R, Lyth D H, et al. False vacuum inflation with Einstein gravity, Phys. Rev. D 1994, 49(12):6410-6433, astro-ph/9401011.
[63] Dine M, Randall L, Thomas S. Supersymmetry Breaking in the Early Universe. Phys. Rev. Lett. 1995, 75(3):398-401, hep-ph/9503303.
[64] Stewart E D. Inflation, supergravity, and superstrings. Phys. Rev. D 1995, 51(12):6847-6853, hep- ph/9405389.
[65] Percival I C, Richards D. Introduction to dynamics, Cambridge University Press (1983).
[66] Lucchin F, Matarrese S. Power-law inflation. Phys. Rev. D 1985, 32(6}:1316-1322.
[67] Kitada Y, Maeda K. Cosmic no-hair theorem in homogeneous spacetimes. I. Bianchi models. Class. Quantum. Grav. 1993, 10(4):703-734.
[68] Sahni V, Wang L. New Cosmological Model of Quintessence and Dark Matter. Phys. Rev. D 2000, 62(10):103517(4), astro-ph/9910097.
[69] Steinhardt P J, Wang L M, Zlatev I. Cosmological tracking solutions. Phys. Rev. D 1999, 59(12):123504(13), astro-ph/9812313.
[70] Ratra B, Peebels P J E. Cosmological Consequences of a Rolling Homogeneous Scalar Field. Phys. Rev. D 1988, 37(12):3406-3427.
[71] Wetterich C, Cosmology, the Fate of Dilatation Symmetry. Nuclear Physics B 1988, 302(4):668-696.
[72] Ferreira P G, Joyce M. Structure Formation with a Self-Tuning Scalar Field. Phys. Rev. Lett. 1997,79(24):4740 - 4743, astro-ph/9707286;
[73] Ferreira P G, Joyce M. Cosmology with a primordial scaling field. Phys. Rev. D 1998, 58(2):023503(23), astro-ph/9711102.
[74] Frieman J, Hill C T, Stebbins A, et al. Cosmology with Ultralight Pseudo Nambu-Goldstone Bosons. Phys. Rev. Lett. 1995, 75(11):2077-2080, astro-ph/9505060.
[75] Brax P, Martin J. Robustness of quintessence. Phys. Rev. D 2000, 61(10):103502(14), astro- ph/9912046.
[76] Sahni V, Starobinsky A A. The Case for a Positive Cosmological Lambda-term. Int. J. Mod. Phys. D 2000, 9(4):373-444, astro-ph/9904398.
[77] Urena-López, L A, Liddle A. Supermassive Black Holes in Scalar Field Galaxy Halos. Phys. Rev. D 2002, 66(8):083005(5), astro-ph/0207493.
[78] Barreiro T, Copeland E J, Nunes N J. Quintessence Arising from Exponential Potentials. Phys. Rev. D 2000, 61(12):127301(4), astro-ph/9910214.
[79] Zlatev I, Wang L, Steinhardt P J. Quintessence, Cosmic Coincidence, and the Cosmological Constant. Phys. Rev. Lett. 1999. 82(2):896-899, astro-ph/9807002.
[80] Albrecht A, Burgess C P, Ravndal F. et al. Natural Quintessence and Large Extra Dimensions. Phys. Rev. D 2002, 65(12):123507(10), astro-ph/0107573.
[81] Sami M, Toporensky A. Phantom Field and the Fate of Universe. Mod. Phys. Lett. A 2004, 19(20):1509-1517, gr-qc/0312009.
[82] Overduin J M. Wesson P S. Kaluza-Klein Gravity. Phys. Rept. 1997, 283(5-6):303-379.
[83] Wesson P S. Space-Time-Matter. Singapore: World Scientific, 1999.
[84] Sabbata de V, Schmutzer E. Unified Field Theories of More Than 4 Dimensions, proc. international school of cosmology and gravitation. Erice, World Scientific, Singapore, 1983.
[85] Lee H C. An Introduction to Kaluza-Klein Theories, proc. Chalk River workshop on Kaluza-Klein theories, Singapore: World Scientific, 1984.
[86] Kang K, Fried H, Frampton P. Fifth workshop on grand unification. Singapore: World Scientific, 1984.
[87] Piran T, Weinberg S. Physics in Higher Dimensions, proc. 2nd Jerusalem winter school of theoretical physics. Singapore: World Scientific, 1986.
[88] Appelquist T, Chodos A, Freund P G 0. Modern Kaluza-Klein Theories. Menlo Park: Addison- Wesley, 1987.
[89] Collins P D B, Martin A D, Squires E J. Particle Physics and Cosmology. New York: Wiley, 1989.
[90] Duff M J, Nilsson B E W, Pope C N. Kaluza-Klein Supergravity. Phys. Rep. 1986, 130(1)1-85.
[91] Bailin D, Love A. Kaluza-Klein Theories. Rep. Prog. Phys. 1987, 50(9):1087-1170.
[92] Duff M J. Kaluza-Klein Theory in Perspective, hep-th/9410046.
[93] Randall L, Sundrum R. An Alternative to Compactification. Phys. Rev. Lett. 1999, 83(23):4690(4), hep-th/9906064.
[94] Randall L, Sundrum R. Large Mass Hierarchy from a Small Extra Dimension. Phys. Rev. Lett. 1999, 83(17):3370(4), hep-ph/9905221.
[95] Kaluza T. Zum Unitatsproblem der Physik. Sitz. Preuss. Akad. Wiss. Phys. Math. 1921 Kl:966
[96] Klein O. Quantentheorie and funfdimensionale Relativitatstheorie. Zeits. Phys. 1926, 37: 859
[97] Bergmann P G. Unified Field Theory with Fifteen Field Variables. Ann. Math. 1948, 49(1):255-264.
[98] Lessner G. Unified field theory on the basis of the projective theory of relativity. Phys. Rev. D 1982, 25(12):3202-3217, gr-qc/0005079.
[99] Liu H Y, Wesson P S. The physical properties of charged five-dimensional black holes. Class. Quant. Grav. 1997, 14(7):1651-1654.
[100] Wesson P S. An Embedding for General Relativity with Variable Rest Mass. Gen. Rel. Grav. 1984, 16(2):193203.
[101] Liu H Y, Mashhoon B. Spacetime measurements in Kaluza-Klein gravity. Phys. Lett. A 2000, 272(1-2):26-31.
[102] Campbell J E. A Course of Differential Geometry. Clarendon: Oxford, 1926.
[103] Guth A H. Inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D 1981, 23(2):347-356.
[104] Linde A D. A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Phys. Lett. B 1982, 108(6):389-393.
[105] Linde A D. Chaotic inflation. Phys. Lett. B 1983, 129(3-4):177-181 .
[106] Coble K, Dodelson S, Frieman J A. Dynamical A models of structure formation. Phys. Rev. D 1997, 55(4):1851-1859, astro-ph/9608122.
[107] Caldwell R R, Steinhardt P J. Imprint of gravitational waves in models dominated by a. dynamical cosmic scalar field. Phys. Rev. D 1998, 57(10):6057-6064, astro-ph/9710062.
[108] Zlatev I, Wang L M, Steinhardt P J. Quintessence, Cosmic Coincidence, and the Cosmological Constant. Phys. Rev. Left. 1999, 82(5):896-899, astro-ph/9807002.
[109] Heard I P C, Wands D. Cosmology with positive and negative exponential potentials. Class. Quant. Grav. 2002, 19(21):5435-5447, gr-qc/0206085.
[110] Guo Z K, Piao Y S, Cai R G et al. Cosmological scaling solutions and cross-coupling exponential potential. Phys. Lett. B 2003, 576(1-2):12-17, hep-th/0306245.
[111] Gno Z K, Piao Y S, Zhang Y Z. Cosmological scaling solutions and multiple exponential potentials. Phys. Lett. B 2003, 568(1-2):1-7, hep-th/0304048.
[112] Liu H Y, Wesson P S. Universe Models with a Variable Cosmological "Constant" and a "Big Bounce". Astrophys. J. 2001, 562(i):1-12, gr-qc/0107093.
[113] Overduin J M, Wesson P S. Kaluza-Klein gravity. Phys. Rep. 1997, 283(5-6):303-378, grqc/9805018.
[114] Chang B R, Liu H Y, Xu L X. Five-Dimensional Cosmological Scaling Solution. Mod. Phys. Lett. A 2005, 20(12):923-928, astro-ph/0405084.
[115] Liu H Y, Mashhoon B. A Machian interpretation of the cosmological constant. Ann.de Physik 1995, 4:565-582.
[116] Liu H Y. Exact Global Solutions of Brane Universe and Big Bounce. Phys. Lett. B, 2003, 560(3-4):149-154, hep-th/0206198.
[117] Wang B L, Liu H Y, Xu L X. Accelerating Universe in a Big Bounce Model. Mod. Phys. Lett. A 2004, 19(6):449-456, gr-qc/0304093.
[118] Xu L X, Liu H Y, Wang B L. On the Big Bounce Singularity of a Simple 5D Cosmological Model. Chin. Phys. Left. 2003, 20(7):995-998, gr-qc/0304049.
[119] Sahni V, Saini T D. Starobinsky A A and Alam U, Statefinder—A new geometrical diagnostic of dark energy. JETP Lett. 2003, 77(5):201-206, astro-ph/0201498.
[120] 张鑫．宇宙学常数与暗能量的若干问题：(博士学位论文)．北京：中国科学院高能物理研究所，2006．
[121] Zimdahl W, Pavon D. Letter: Statefinder Parameters for Interacting Dark Energy. Gen. Rel. Gray. 2004, 36(6):1483-1491, gr-qc/0311067.
[122] Alam U, Sahni V, Saini T D et al. Exploring the expanding Universe and dark energy using the statefinder diagnostic. Mon. Not. Roy. Astron. Soc. 2003, 344(4):1057-1074, astro-ph/0303009.
[123] Gorini V, Kamenshchik A, Moschella U. Can the Chaplygin gas be a plausible model for dark energy? Phys. Rev. D 2003, 67(6):063509(5), astro-ph/0209395.
[124] Zhang X. Statefinder diagnostic for coupled quintessence. Phys. Lett. B 2005, 611(1-2):1-7, astro-ph/0503075.
[125] Zhang X. Statefinder Diagnostic for Holographic Dark Energy Model. Int. J. Mod. Phys. D 2005, 14(09):1597-1606, astro-ph/0504586.
[126] Wu P X, Yu H W. Statefinder Parameters for Quintom Dark Energy Model. Int. J. Mod. Phys. D 2005, 14(11):1873-1881, gr-qc/0509036.
[127] Zhang X, Wu F Q, Zhang J F. New generalized Chaplygin gas as a scheme for unification of dark energy and dark matter. JCAP 2006, 06(01):003, astro-ph/0411221.
[128] Setare M R, Zhang J F, Zhang X. Statefinder diagnosis in a non-flat universe and the holographic model of dark energy. JCAP 2007, 07(03):007, gr-qc/0611084.
[129] Zlatev I, Steinhardt P J. A tracker solution to the cold dark matter cosmic coincidence problem. Phys. Lett. B 1999, 459(4):570-574, astro-ph/9906481.
[130] Ratra B, Peebels P J E. Cosmological consequences of a roiling homogeneous scalar field. Phys. Rev. D 1988, 37(12):3406-3427.
[131] Chang B R, Liu H Y, Xu L X et al. Statefinder Parameters for Quintessence with Tracker Potential. submitted to Prog. Theor. Phys.
[132] Guo Z K, Zhang Y Z. Interacting phantom energy. Phys. Rev. D 2005, 71(2):023501(5), astro-ph/0411524.
[133] Guo Z K, Cai R G, Zhang Y Z. Cosmological evolution of interacting phantom energy with dark matter. JCAP 2005, 05(05):002, astro-ph/0412624.
[134] Liu H Y, Liu H Y, Chang B R et al. Induced Phantom and 5D Attractor Solution in SpacetimeMatter Theory. Mod. Phys. Lett. A 2005, 20(26):1973-1982, gr-qc/0504021.
[135] Chang B R, Liu H Y, Xu L X et al. Statefinder Diagnostic for Phantom Model with V(φ) = V_0 exp(-λφ~2). Chin. Phys. Lett 2007, 24(7):2153-2156, arXiv:0704.3768.
[136] Guo Z K, Piao Y S, Zhang X M et al. Cosmological evolution of a quintom model of dark energy. Phys. Lett. B 2005, 608(3-4):177-182, astro-ph/0410654.
[137] Hao J G, Li X Z. Phantom cosmic dynamics: Tracking attractor and cosmic doomsday. Phys. Rev. D 2004, 70:043529(7), astro-ph/0309746.
[138] Chang B R, Liu H Y, Xu LX et al. Statefinder parameters for interacting phantom energy with dark matter. JCAP 2007, 07(01):016, astro-ph/0612616.
[139] Liko T, Wesson P S. The Big Bang as a Phase Transition. Int. J. Mod. Phys. A 2005, 20(10):2037-2045, gr-qc/0310067;
[140] Xu L X, Liu H Y. Three Components Evolution in a Simple Big Bounce Cosmological Model. Int. J. Mod. Phys. D 2005, 14 (5):883-892, astro-ph/0412241.
[141] Xu L X, Liu H Y. Scaling Dark Energy in a Five-Dimensional Bouncing Cosmological Model. Int. J. Mod. Phys. D 2005, 14(11):1947-1957, astro-ph/0507250.
[142] Xu L X, Liu H Y, Chang B R. Correspondence Between 5D Ricci-Flat Cosmological Models and Quintessence Dark Energy Models. Mod. Phys. Lett. A. 2006, 21(40):3105-3114, astro-ph/0507397.
[143] Xu L X, Liu H Y, Zhang C W. Reconstruction of 5D Cosmological Models from the Equation of State of Dark Energy. Int. J. Mod. Phys. D 2006, 15(2):215-224, astro-ph/0510673.
[144] Xu L X, Liu H Y, Ping Y L. Reconstruction of Five-dimensional Bounce cosmological Models From Deceleration Factor. Int. J. Theor. Phys. 2006, 45(4):843-850, astro-ph/0601471.
[145] Zhang C W, Liu H Y, Xu L X et al. Universe Evolution in a 5D Ricci-Flat Cosmology. Mod. Phys. Lett. A 2006, 21(7): 571-580, astro-ph/0602414.
[146] Ping Y L, Liu H Y, Xu L X. Using (4+1) Split and Energy Conditions to Study the Induced Matter in 5D Ricci-Flat Cosmology. Int. J. Mod. Phys. A2 007, 22(5):985-994, gr-qc/0610094.
[147] Liu M L, Liu H Y, Xu L X et al. Radiation and Potential Barriers of a 5D Black String Solution. Mod. Phys. Lett. A 2006, 21(39):2937-2945, gr-qc/0611137.
[148] Chang B R, Liu H Y, Xu L X et al. Statefinder Parameters for Five-Dimensional Cosmology. To be published in Mod. Phys. Lett. A.
[149] Hao J G, Li X Z. Constructing dark energy models with a late time de Sitter attractor. Phys. Rev. D 2003, 68(8):083514(7), hep-th0306033;
[150] Guo Z K, Piao Y S, Zhang Y Z. Attractor behavior of phantom cosmology. Phys. Lett. B 2004, 594(3-4):247-251, astro-ph/0404225. Notation: astro-ph/, hep-th/, gr-qc/please see http://Arxiv.org/abs/xx-xx/xxxxxxx.