加速膨胀宇宙中的若干问题研究
|
摘要
宇宙加速膨胀的发现,对现代物理理论提出了新的挑战,也对科学计算赋予了新的任务。当前,人类已经进入了精确宇宙学时代,这是以下述事实为标志的:利用大量观测数据,通过数值方法计算出精确结果,比较各类理论的异同点,选取其中最佳者。本文利用数值计算和解析方法,探讨了宇宙加速膨胀的一些相关问题,研究了两种加速宇宙模型,它们分别是粘滞Cardassian宇宙和标量挠率宇宙。
本文由五个部分组成。我们首先介绍了宇宙的一些基本事实以及基于广义相对论的宇宙学基础,还对加速宇宙模型做了简单分类。在第二章中,我们讨论了粘滞Cardassian宇宙模型的动力学和位力化。动力学分析结果表明:引入粘滞系数后,相空间存在一条临界线。与没有粘滞的情况相比,PL模型态方程参数叫ω_(eff)可以穿越-1,不再是常数。对MP和Exp模型来说,ω_(eff)在演化过程中比没有粘滞的情况更接近于-1。由位力化的研究可知,粘滞还可以减缓星系结团。我们在第三章中讨论了标量挠率宇宙。标量挠率模的动力学自治方程组存在一个晚期de Sitter吸引子,相图是一族异宿轨线,这很大程度上缓解了精调问题。我们发现标量挠率宇宙的Statefinder的参数演化具有一些特别的性质,由此可以将此模型与其它模型区分。对应于动力学分析,Statefinder把参数α_1分成不同取值范围。更进一步的讨论表明,Statefinder与动力学分析相比,可以简便地区分不同模型,但是后者却能提供更多的信息。在第四章中,我们用SNeIa数据分别对粘滞Cardassian模型和标量挠率模型进行了参数拟合,给出了参数的最佳拟合值。最后,我们对本文进行了总结,并展望了未来的工作。
The discovery of accelerating expansion of the universe imposes a great new challenge to the modern theory of physics and entrust a new mission to the scientific computation. Nowadays, human beings have entered into an era of precise cosmology: using the latest astronomical observations data, by the numerical method, calculate precise results and compare various theories, then give the best one. The current work explores some problems relevant to accelerating expansion of the universe by the numerical computation method and analytic method. We study two kinds of accelerating expansion theory which are viscous Cardassian universe and scalar torsion cosmology, respectively.
The entire dissertation is divided into five chapters. We begin by giving some basic facts about our universe and the fundamental theory of cosmology based on the general relativity in Chapter 1. Besides, we review the classification of various accelerating cosmology models briefly. In Chapter 2, we discuss the dynamics and virialization of the viscous Cardassian models. The dynamical analysis indicates that there exists a singular curve in the phase space of viscous Cardassian model. In the viscous PL model, the equation-of-state parameter w_(eff) is no longer a constant and it can cross the cosmological constant divide w_∧= - 1, in contrast with same problem of the ordinary PL model. For MP and Exp models, w_(eff) evolves more near -1 than the case without viscosity. The virialization results show that the bulk viscosity retards the progress of collapse system. In Chapter 3 the torsion cosmology is studied. The dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. We find that there are some typical characteristic of the evolution of statefinder parameters for the torsion cosmology that can be distinguished from the other cosmological models. The statefinder diagnostic divides the torsion parameter a_1 into differential ranges, which is in keeping with the requirement of dynamical analysis. Further discussion implies that the statefinder diagnostic has the advantage over the dynamical analysis at the simplicity, but the latter can provide more information. In Chapter 4, we fit the viscous Cardassian models and scalar torsion model to supernovae data and give the best fit values of the parameters. In the end, we give a conclusion and prospect.
本文由五个部分组成。我们首先介绍了宇宙的一些基本事实以及基于广义相对论的宇宙学基础,还对加速宇宙模型做了简单分类。在第二章中,我们讨论了粘滞Cardassian宇宙模型的动力学和位力化。动力学分析结果表明:引入粘滞系数后,相空间存在一条临界线。与没有粘滞的情况相比,PL模型态方程参数叫ω_(eff)可以穿越-1,不再是常数。对MP和Exp模型来说,ω_(eff)在演化过程中比没有粘滞的情况更接近于-1。由位力化的研究可知,粘滞还可以减缓星系结团。我们在第三章中讨论了标量挠率宇宙。标量挠率模的动力学自治方程组存在一个晚期de Sitter吸引子,相图是一族异宿轨线,这很大程度上缓解了精调问题。我们发现标量挠率宇宙的Statefinder的参数演化具有一些特别的性质,由此可以将此模型与其它模型区分。对应于动力学分析,Statefinder把参数α_1分成不同取值范围。更进一步的讨论表明,Statefinder与动力学分析相比,可以简便地区分不同模型,但是后者却能提供更多的信息。在第四章中,我们用SNeIa数据分别对粘滞Cardassian模型和标量挠率模型进行了参数拟合,给出了参数的最佳拟合值。最后,我们对本文进行了总结,并展望了未来的工作。
The discovery of accelerating expansion of the universe imposes a great new challenge to the modern theory of physics and entrust a new mission to the scientific computation. Nowadays, human beings have entered into an era of precise cosmology: using the latest astronomical observations data, by the numerical method, calculate precise results and compare various theories, then give the best one. The current work explores some problems relevant to accelerating expansion of the universe by the numerical computation method and analytic method. We study two kinds of accelerating expansion theory which are viscous Cardassian universe and scalar torsion cosmology, respectively.
The entire dissertation is divided into five chapters. We begin by giving some basic facts about our universe and the fundamental theory of cosmology based on the general relativity in Chapter 1. Besides, we review the classification of various accelerating cosmology models briefly. In Chapter 2, we discuss the dynamics and virialization of the viscous Cardassian models. The dynamical analysis indicates that there exists a singular curve in the phase space of viscous Cardassian model. In the viscous PL model, the equation-of-state parameter w_(eff) is no longer a constant and it can cross the cosmological constant divide w_∧= - 1, in contrast with same problem of the ordinary PL model. For MP and Exp models, w_(eff) evolves more near -1 than the case without viscosity. The virialization results show that the bulk viscosity retards the progress of collapse system. In Chapter 3 the torsion cosmology is studied. The dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. We find that there are some typical characteristic of the evolution of statefinder parameters for the torsion cosmology that can be distinguished from the other cosmological models. The statefinder diagnostic divides the torsion parameter a_1 into differential ranges, which is in keeping with the requirement of dynamical analysis. Further discussion implies that the statefinder diagnostic has the advantage over the dynamical analysis at the simplicity, but the latter can provide more information. In Chapter 4, we fit the viscous Cardassian models and scalar torsion model to supernovae data and give the best fit values of the parameters. In the end, we give a conclusion and prospect.
引文
[1]Hubble E.,A relation between distance and radial velocity among extragalatic nebulae,Proc Nat Acad Sci U S[J],1929,15:168
[2]Riess A.G.,et al.,Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,Astron.J.[J],1998,116:1009-1038
[3]Perlmutter S.,et al.,Measurements of Omega and Lambda from 42 high redshift supernovae,Astrophys.J.[J],1999,517:565-586
[4]Tonry J.L.,et al.,Cosmological results from high-z supernovae,Astrophys.J.[J],2003,594:1-24
[5]Riess A.G.,et al.,Type Ia supernova discoveries at z＞1 from the Hubble Space Telescope:Evidence for past deceleration and constraints on dark energy evolution,Astrophys.J.[J],2004,607:665-687
[6]Choudhury T.R.and Padmanabhan T.,Cosmological parameters from supernova observations:A critical comparison of three data sets,Astron.Astrophys.[J],2005,429:807
[7]Gamow G.,Prescient paper predicting the existence of a uniform and diffuse relic radiation field from the Hot Big Bang,Phy Rev[J],1946,70:572
[8]Dicke R.H.,et al.,Cosmic-black-body radiation,ApJ[J],1965,142:414
[9]Penzias A.A.,Wilson R.W.,A measurement of excess antenna temperature at 4080 Mc/s,ApJ[J],1965,142:419
[10]Freedman W.L.and Turner M.S.,Measuring and Understanding the Universe,Rev.Mod.Phys.[J],2003,75:1433-1447
[11]Martinez V.J.,Introductory review to the historical development of modern cosmology,Historical Development of Modern Cosmology,A.S.P.Conf.Set.vol.252,(2001),eds.V.J.Martinez,V.Trimble,and M.J.Pons-Borderia,pp.1-9
[12]Weinberg S.,Gravitation and Cosmology:Principles and Applications of the General Theory of Relativity[M],John Wiley,1972
[13]刘辽,赵峥,广义相对论(第二版)[M],北京:高等教育出版社,2004
[14]俞允强,热大爆炸宇宙学[M],北京:北京大学出版社,2003
[15]李新洲,暗能量,科学(双月刊)[J],第55卷,第6期2003
[16]李新洲,孙珏岷,宇宙的构成和哥白尼原理,自然杂志[J],第27卷,第1期2005
[17]Ratra B.and Peebles P.J.E.,Cosmological Consequences of a Rolling Homogeneous Scalar Field,Phys.Rev.[J],1988,D37:3406
[18]Coble K.,Dodelson S.and Frieman J.A.,Dynamical Lambda models of structure formation,Phys.Rev.[J],1997,D55:1851-1859
[19]Caldwell R.R.,Dave R.and Steinhardt J.,Cosmological imprint of an energy component with general equation of state,Phys.Rev.Lett.[J],1998,80:1582-1585
[20]Li X.Z.,Hao J.G.and Liu D.J,Quintessence with O(N) symmetry,Class.Quant.Grav.[J],2002,19:6049-6058
[21]Li X.Z.,nao J.G.and Liu D.J,Can Quintessence Be The Rolling Tachyon?,Chin.Phys.Lett.[J],2002,19:1584
[22]Peebles P.J.E.and Ratra B.,The Cosmological constant and dark energy,Rev.Mod.Phys.[J],2003,75:559-606
[23]Padmannabhan T.,Cosmological constant:The Weight of the vacuum,Phys.Rept.[J],2003,380:235-320
[24]Caldwell R.R.,A Phantom menace?,Phys.Lett.[J],2002,B545:23-29
[25]Hao J.G.and Li X.Z.,Cosmological dynamics of scalar fields with O(N) symmetry,Class.Quant.Grav.[J],2004,21:4771-4779
[26]Hao J.G.and Li X.Z.,An Attractor solution of phantom field,Phys.Rev.[J],2003,D67:107303
[27]Hao J.G.and Li X.Z.,Constructing dark energy models with late time de Sitter attractor,Phys.Rev.[J],2003,D68:083514
[28]Hao J.G.and Li X.Z.,Phantom cosmic dynamics:Tracking attractor and cosmic doomsday,Phys.Rev.[J],2004,DT0:043529
[29]Li X.Z.,Zhao Y.B.and Sun C.B.,Heteroclinic orbit and tracking attractor in cosmological model with a double exponential potential,Class.Quant.Grav.[J],2005,22:3759-3766
[30]孙昌波,赵一斌,孙珏岷,具有双指数势的phantom宇宙学,上海师范大学学报(自然科学版)[J],2005,第34卷,第1期
[31]Armendariz-Picon A.,Mukhanov V.F.and Steinhardt.P.J.,A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration,Phys.Rev.Lett.[J],2000,85:4438-4441
[32]Khoury J.and Weltman A.,Chameleon cosmology,Phys.Rev.[J],2004,D69:044026
[33]Bento M.C.,Bertolami O.and Sen A.A.,Phys.Rev.[J],2002,D66:043507
[34]Zhao G.B.,et al.,Perturbations of the quintom models of dark energy and the effects on observations,Phys.Rev.[J],2005,D72:123515
[35]Ratra B.and Peebles P.J.E.,Cosmological Consequences of a Rolling Homogeneous Scalar Field,Phys.Rev.[J],1988,D37:3406
[36l Fujii Y.and Maeda K.,The scalar-tensor theory of gravitation[M],Cambridge:Cambridge University Press,2003
[37]Buchdahl H.A.,MNRAS[J]1970,150:1
[38]Shie K.F.,Nester J.M.and Yo H.J.,Torsion Cosmology and the Accelerating Universe,Phys.Rev.[J],2008,D78:023522
[39]Yo H.J.and Nester J.M.,Dynamic Scalar Torsion and an Oscillating Universe,Mod.Phys.Lett.[J],2007,A22:2057-2069
[40]Freese K.and Lewis M.,Cardassian expansion:A Model in which the universe is flat,matter dominated,and accelerating,Phys.Lett.[J],2002,B540:1-8
[41]Freese K.,Generalized Cardassian Expansion:Models in Which the Universe is Flat,Matter Dominated,and Accelerating,Nucl.Phys.[J],2003,B124:50-54
[42]Gondolo P.and Freese K.,Fluid Interpretation of Cardassian Expansion,Phys.Rev.[J],2003,D68:063509
[43]Liu D.J.,Sun C.B.and Li X.Z.,Exponential Cardassian Universe,Phys.Lett.[J],2006,B634:442-447
[44]SUN Chang-bo,Cardassian model with matter and radiation,上海:上海师范大学学报[J],2008,37(1):40-45
[45]孙昌波硕士论文,Friedmann方程与宇宙加速膨胀的研究,上海:上海师范大学,2006
[46]孙祖尧博士论文,暗能量相关问题的研究,上海:中国科学院上海天文台,2007
[47]金兴华博士论文,暗能量和暗物质及其观测效应研究,上海:上海师范大学,2007
[48]Balbus A.P.,A Powerful viscous shear instability in weakly magnetized,dilute plasmas,Astrophys.J.[J],2004,616:857-864
[49]Pratt S.,Formulating viscous hydrodynamics for large velocity gradients,Phys.Rev.[J],2008,C77:024910
[50]Landau L.D.and Lifshitz E.M.,Fluid Mechanics[M],Butterworth Heinemann,1987
[51]Israel W.,Nonstationary irreversible thermodynamics:A Causal relativistic theory,Annals Phys.[J],1976,100:310-331
[52]Harko T.and Mak M.K.,Viscous Bianchi type Ⅰ universes in brane cosmology,Class.Quant.Grav.[J],2003,20:407-422
[53]Cataldo M.,Cruz N.and Lepe S.,Viscous dark energy and phantom evolution,Phys.Lett.[J],2005,B619:5-10
[54]Zhai X.H.,Xu Y.D.and Li X.Z.,Viscous generalized Chaplygin gas,Int.J.Mod.Phys.[J],2006,D15:1151-1162
[55]Colistete R.,Fabris J.C.,Tossa J.and Zimdahl W.,Bulk Viscous Cosmology,Phys.Rev.[J],2007,D76:103516
[56]Folomeev V.and Gurovich V.,Viscous dark fluid,Phys.Lett.[J],2008,B661:75-77
[57]Belinsky V.A.and Khalatnikov I.M.,Sov.Phys.JETP.[J],1977,45:1
[58]Sun C.B.,Wang J.L.and Li X.Z.,Viscous Cardassian universe,accepted in IJMPD[J],2009
[59]Gunn J.E.and Gott J.R.,On the infall of matter into cluster of galaxies and some effects on their evolution,Astrophys.J.[J],1972,176:1-19
[60]Maor I.and Lahav O.,On virialization with dark energy,JCAP[J],2005,0507:003
[61]Press W.H.et al.,C数值算法(中文版),北京:电子工业出版社,2004
[62]Nesseris A.and Perivolaropoulos L.,A Comparison of cosmological models using recent supernova data,Phys.Rev.[J],2004,DT0:043531
[63]Riess A.G.et al.,New Hubble Space Telescope Discoveries of Type Ia Supernovae at z＞=1:Narrowing Constraints on the Early Behavior of Dark Energy,Astrophys.J.[J],2007,659:98-121
[64]Hehl F.W.,Heyde P.,Kerlik G.D.,and Nester J.M.,General Relativity with Spin and Torsion:Foundations and Prospects,Rev.Mod.Phys.[J],1976,48:393
[65]Nester J.M.,"Gravity,torsion and Gauge theory",in Introduction to Kaluza-Klein theories[M],Singapore:World Scientific,1984,pp 83-115.
[66]Hehl F.W.,in Proc.of 6th Course of the International School of Cosmology and Gravitation on Spin,Torsion and Supergravity[M],New York:Plenum,1980 p5
[67]Hayashi K.and Shirafuji T.,Prog.Wheor.Phys.[J],Gravity from Poincare Gauge Theory of the Fundamental Particles,1980 64:866,883,1435,2222
[68]Hehl F.W.,McCrea J.D.,Mielke E.W.and Neeman Y,Metric affine gauge theory of gravity:Field equations,Noether identities,world spinors,and breaking of dilation invariance,Phys.Rept.1995,258:1-171
[69]Mielke E.W.,Geometrodynamics of Gauge Fields[M],Berlin:Akademie-Verlag,1987
[70]Gronwald F.and Hehl F.W.,"On the Gauge Aspects of Gravity" in Proc.14th Course of the School of Gravitation and Cosmology(Erice)[R],Singapore:World Scientific,1996 pp 148-98,arXiv:gr-qc/9701054.
[71]Blagojevic M.,Gravitation and Gauge Symmetries[M],Bristol:Institute of Physics,2002
[72]Kopczynski W.,Phys.Lett.[J],1972,A39,219-220;Phys.Lett.[J],1973,A43,63-64
[73]Li X.Z.,Sun C.B.and Xi P.,Torsion cosmological dynamics,Phys.Rev.[J],2009,D79:027301
[74]Sahni V.,Saini T D.,Starobinsky A.A.and Alam U.,Statefinder:A New geometrical diagnostic of dark energy,JETP Lett.[J],2003,77:201
[75]Li X.Z.,Sun C.B.and Xi P.,Statefinder diagnostic in a torsion cosmology,accepted in JCAP[J],2009
[76]Davis T.M.et al.,Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes,Astrophys.J.[J],2007,666:716
[2]Riess A.G.,et al.,Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,Astron.J.[J],1998,116:1009-1038
[3]Perlmutter S.,et al.,Measurements of Omega and Lambda from 42 high redshift supernovae,Astrophys.J.[J],1999,517:565-586
[4]Tonry J.L.,et al.,Cosmological results from high-z supernovae,Astrophys.J.[J],2003,594:1-24
[5]Riess A.G.,et al.,Type Ia supernova discoveries at z＞1 from the Hubble Space Telescope:Evidence for past deceleration and constraints on dark energy evolution,Astrophys.J.[J],2004,607:665-687
[6]Choudhury T.R.and Padmanabhan T.,Cosmological parameters from supernova observations:A critical comparison of three data sets,Astron.Astrophys.[J],2005,429:807
[7]Gamow G.,Prescient paper predicting the existence of a uniform and diffuse relic radiation field from the Hot Big Bang,Phy Rev[J],1946,70:572
[8]Dicke R.H.,et al.,Cosmic-black-body radiation,ApJ[J],1965,142:414
[9]Penzias A.A.,Wilson R.W.,A measurement of excess antenna temperature at 4080 Mc/s,ApJ[J],1965,142:419
[10]Freedman W.L.and Turner M.S.,Measuring and Understanding the Universe,Rev.Mod.Phys.[J],2003,75:1433-1447
[11]Martinez V.J.,Introductory review to the historical development of modern cosmology,Historical Development of Modern Cosmology,A.S.P.Conf.Set.vol.252,(2001),eds.V.J.Martinez,V.Trimble,and M.J.Pons-Borderia,pp.1-9
[12]Weinberg S.,Gravitation and Cosmology:Principles and Applications of the General Theory of Relativity[M],John Wiley,1972
[13]刘辽,赵峥,广义相对论(第二版)[M],北京:高等教育出版社,2004
[14]俞允强,热大爆炸宇宙学[M],北京:北京大学出版社,2003
[15]李新洲,暗能量,科学(双月刊)[J],第55卷,第6期2003
[16]李新洲,孙珏岷,宇宙的构成和哥白尼原理,自然杂志[J],第27卷,第1期2005
[17]Ratra B.and Peebles P.J.E.,Cosmological Consequences of a Rolling Homogeneous Scalar Field,Phys.Rev.[J],1988,D37:3406
[18]Coble K.,Dodelson S.and Frieman J.A.,Dynamical Lambda models of structure formation,Phys.Rev.[J],1997,D55:1851-1859
[19]Caldwell R.R.,Dave R.and Steinhardt J.,Cosmological imprint of an energy component with general equation of state,Phys.Rev.Lett.[J],1998,80:1582-1585
[20]Li X.Z.,Hao J.G.and Liu D.J,Quintessence with O(N) symmetry,Class.Quant.Grav.[J],2002,19:6049-6058
[21]Li X.Z.,nao J.G.and Liu D.J,Can Quintessence Be The Rolling Tachyon?,Chin.Phys.Lett.[J],2002,19:1584
[22]Peebles P.J.E.and Ratra B.,The Cosmological constant and dark energy,Rev.Mod.Phys.[J],2003,75:559-606
[23]Padmannabhan T.,Cosmological constant:The Weight of the vacuum,Phys.Rept.[J],2003,380:235-320
[24]Caldwell R.R.,A Phantom menace?,Phys.Lett.[J],2002,B545:23-29
[25]Hao J.G.and Li X.Z.,Cosmological dynamics of scalar fields with O(N) symmetry,Class.Quant.Grav.[J],2004,21:4771-4779
[26]Hao J.G.and Li X.Z.,An Attractor solution of phantom field,Phys.Rev.[J],2003,D67:107303
[27]Hao J.G.and Li X.Z.,Constructing dark energy models with late time de Sitter attractor,Phys.Rev.[J],2003,D68:083514
[28]Hao J.G.and Li X.Z.,Phantom cosmic dynamics:Tracking attractor and cosmic doomsday,Phys.Rev.[J],2004,DT0:043529
[29]Li X.Z.,Zhao Y.B.and Sun C.B.,Heteroclinic orbit and tracking attractor in cosmological model with a double exponential potential,Class.Quant.Grav.[J],2005,22:3759-3766
[30]孙昌波,赵一斌,孙珏岷,具有双指数势的phantom宇宙学,上海师范大学学报(自然科学版)[J],2005,第34卷,第1期
[31]Armendariz-Picon A.,Mukhanov V.F.and Steinhardt.P.J.,A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration,Phys.Rev.Lett.[J],2000,85:4438-4441
[32]Khoury J.and Weltman A.,Chameleon cosmology,Phys.Rev.[J],2004,D69:044026
[33]Bento M.C.,Bertolami O.and Sen A.A.,Phys.Rev.[J],2002,D66:043507
[34]Zhao G.B.,et al.,Perturbations of the quintom models of dark energy and the effects on observations,Phys.Rev.[J],2005,D72:123515
[35]Ratra B.and Peebles P.J.E.,Cosmological Consequences of a Rolling Homogeneous Scalar Field,Phys.Rev.[J],1988,D37:3406
[36l Fujii Y.and Maeda K.,The scalar-tensor theory of gravitation[M],Cambridge:Cambridge University Press,2003
[37]Buchdahl H.A.,MNRAS[J]1970,150:1
[38]Shie K.F.,Nester J.M.and Yo H.J.,Torsion Cosmology and the Accelerating Universe,Phys.Rev.[J],2008,D78:023522
[39]Yo H.J.and Nester J.M.,Dynamic Scalar Torsion and an Oscillating Universe,Mod.Phys.Lett.[J],2007,A22:2057-2069
[40]Freese K.and Lewis M.,Cardassian expansion:A Model in which the universe is flat,matter dominated,and accelerating,Phys.Lett.[J],2002,B540:1-8
[41]Freese K.,Generalized Cardassian Expansion:Models in Which the Universe is Flat,Matter Dominated,and Accelerating,Nucl.Phys.[J],2003,B124:50-54
[42]Gondolo P.and Freese K.,Fluid Interpretation of Cardassian Expansion,Phys.Rev.[J],2003,D68:063509
[43]Liu D.J.,Sun C.B.and Li X.Z.,Exponential Cardassian Universe,Phys.Lett.[J],2006,B634:442-447
[44]SUN Chang-bo,Cardassian model with matter and radiation,上海:上海师范大学学报[J],2008,37(1):40-45
[45]孙昌波硕士论文,Friedmann方程与宇宙加速膨胀的研究,上海:上海师范大学,2006
[46]孙祖尧博士论文,暗能量相关问题的研究,上海:中国科学院上海天文台,2007
[47]金兴华博士论文,暗能量和暗物质及其观测效应研究,上海:上海师范大学,2007
[48]Balbus A.P.,A Powerful viscous shear instability in weakly magnetized,dilute plasmas,Astrophys.J.[J],2004,616:857-864
[49]Pratt S.,Formulating viscous hydrodynamics for large velocity gradients,Phys.Rev.[J],2008,C77:024910
[50]Landau L.D.and Lifshitz E.M.,Fluid Mechanics[M],Butterworth Heinemann,1987
[51]Israel W.,Nonstationary irreversible thermodynamics:A Causal relativistic theory,Annals Phys.[J],1976,100:310-331
[52]Harko T.and Mak M.K.,Viscous Bianchi type Ⅰ universes in brane cosmology,Class.Quant.Grav.[J],2003,20:407-422
[53]Cataldo M.,Cruz N.and Lepe S.,Viscous dark energy and phantom evolution,Phys.Lett.[J],2005,B619:5-10
[54]Zhai X.H.,Xu Y.D.and Li X.Z.,Viscous generalized Chaplygin gas,Int.J.Mod.Phys.[J],2006,D15:1151-1162
[55]Colistete R.,Fabris J.C.,Tossa J.and Zimdahl W.,Bulk Viscous Cosmology,Phys.Rev.[J],2007,D76:103516
[56]Folomeev V.and Gurovich V.,Viscous dark fluid,Phys.Lett.[J],2008,B661:75-77
[57]Belinsky V.A.and Khalatnikov I.M.,Sov.Phys.JETP.[J],1977,45:1
[58]Sun C.B.,Wang J.L.and Li X.Z.,Viscous Cardassian universe,accepted in IJMPD[J],2009
[59]Gunn J.E.and Gott J.R.,On the infall of matter into cluster of galaxies and some effects on their evolution,Astrophys.J.[J],1972,176:1-19
[60]Maor I.and Lahav O.,On virialization with dark energy,JCAP[J],2005,0507:003
[61]Press W.H.et al.,C数值算法(中文版),北京:电子工业出版社,2004
[62]Nesseris A.and Perivolaropoulos L.,A Comparison of cosmological models using recent supernova data,Phys.Rev.[J],2004,DT0:043531
[63]Riess A.G.et al.,New Hubble Space Telescope Discoveries of Type Ia Supernovae at z＞=1:Narrowing Constraints on the Early Behavior of Dark Energy,Astrophys.J.[J],2007,659:98-121
[64]Hehl F.W.,Heyde P.,Kerlik G.D.,and Nester J.M.,General Relativity with Spin and Torsion:Foundations and Prospects,Rev.Mod.Phys.[J],1976,48:393
[65]Nester J.M.,"Gravity,torsion and Gauge theory",in Introduction to Kaluza-Klein theories[M],Singapore:World Scientific,1984,pp 83-115.
[66]Hehl F.W.,in Proc.of 6th Course of the International School of Cosmology and Gravitation on Spin,Torsion and Supergravity[M],New York:Plenum,1980 p5
[67]Hayashi K.and Shirafuji T.,Prog.Wheor.Phys.[J],Gravity from Poincare Gauge Theory of the Fundamental Particles,1980 64:866,883,1435,2222
[68]Hehl F.W.,McCrea J.D.,Mielke E.W.and Neeman Y,Metric affine gauge theory of gravity:Field equations,Noether identities,world spinors,and breaking of dilation invariance,Phys.Rept.1995,258:1-171
[69]Mielke E.W.,Geometrodynamics of Gauge Fields[M],Berlin:Akademie-Verlag,1987
[70]Gronwald F.and Hehl F.W.,"On the Gauge Aspects of Gravity" in Proc.14th Course of the School of Gravitation and Cosmology(Erice)[R],Singapore:World Scientific,1996 pp 148-98,arXiv:gr-qc/9701054.
[71]Blagojevic M.,Gravitation and Gauge Symmetries[M],Bristol:Institute of Physics,2002
[72]Kopczynski W.,Phys.Lett.[J],1972,A39,219-220;Phys.Lett.[J],1973,A43,63-64
[73]Li X.Z.,Sun C.B.and Xi P.,Torsion cosmological dynamics,Phys.Rev.[J],2009,D79:027301
[74]Sahni V.,Saini T D.,Starobinsky A.A.and Alam U.,Statefinder:A New geometrical diagnostic of dark energy,JETP Lett.[J],2003,77:201
[75]Li X.Z.,Sun C.B.and Xi P.,Statefinder diagnostic in a torsion cosmology,accepted in JCAP[J],2009
[76]Davis T.M.et al.,Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes,Astrophys.J.[J],2007,666:716