指数势胚宇宙动力学的研究
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摘要
自从上世纪四十年代末Gamow建立大爆炸宇宙学以来,人们对这门新兴学科的追求和探索从未止步。随着近年来实验观测数据的日积月累,人们对宇宙的认识达到了一个相对成熟的程度,并逐渐建立起一个由奇点大爆炸到早期宇宙暴涨再到现在由暗能量和物质共同主导的现代宇宙学模型。尽管如此,宇宙学中还有许多疑问等待科学家们去解决,其中最重要的问题之一是暗能量问题。现代实验数据已充分表明了它的存在性,但由于无法直接观测,人们对暗能量的性质及演化一直众说纷纭,于是也就有了各种各样的暗能量模型。
本文着重研究一类近年来颇受关注的暗能量模型:胚世界暗能量模型。在胚世界宇宙学框架下,我们所生存的四维宇宙被认为是镶嵌在更高维的时空中,而引力相互作用可以在整个高维时空中传播。额外维度给宇宙学带来的效应目前无法被实验精确观测,因而也可能产生各种各样有趣和有意义的预言。这成为宇宙学家们为之不懈追求的动力之一。
在胚世界框架下建立的宇宙学暗能量模型也是丰富多样的,本文主要讨论其中最为流行的两类模型——RS2模型和DGP模型。全文结构如下:第一、二章简单回顾一下宇宙学几十年来的发展概况以及实验观测所取得的成果;第三章归纳宇宙学在暗能量理论方面取得的成果,并简单介绍几种最具代表性的暗能量模型;第四章将概括胚宇宙学的发展,从ADD模型的提出,到RS模型的引入,乃至现在倍受关注的DGP模型;第五、六章将详细分析RS2及DGP两种模型的宇宙学性质,尤其是对含指数势的这两种模型的演化行为进行了深入的动力学分析研究。我们观察到由指数势产生的动力学吸引子,可以使模型的后期行为对初始条件不敏感,从而有效的避免了精调问题。我们还发现标准DGP模型带来的晚期宇宙自加速膨胀,使其有效状态方程小于-1,而第二类DGP模型在暗能量存在的情况下,通过引力修正使宇宙演化的有效状态方程穿越了-1,或趋于-1。这些结果都非常的有意思,能够很好的与今天的天体实验观测符合,给出加速膨胀的宇宙的解释,从而预测未来的宇宙演化。
Since Gamow proposed the explosion cosmology in the end of 1940s, people never stop studying on this new subject. With the development of the observation, we get more and more accurate data and realize that the universe is dominated by the dark energy and dark matter. Though the observation data shows the existence of the dark energy, we can’t observe it directly. The nature of the dark energy remains a mystery. Various models of dark energy have been proposed.
In this paper, we investigate some interesting models of dark energy, especially the brane scenario, in which our four dimensional universe is embedded in a higher dimensional spacetime where the gravitation can propagate in. Since the effect of the extradimension can’t be obtained by experiment exactly, the brane world models admit a much wider range of possibilities for dark energy. It forces the scientists to untie the mystery.
There are lots of dark energy models under the framework of brane world scenario. In this paper we will mainly discuss the Randall-Sundrum2 model and the Dvali-Gabadadze-Porrati model. The structure of the paper is arranged as follows:
In chapter1&2, I review the history of the universe and the result of observation;
In chapter3, I report the achievement in theoretical study of dark energy,emphasizing on several typical models;
In chapter 4, I study the development of the brane scenario and summarize several major brane models;
The main work of this thesis is in chapter 5&6 in which I describe the property of RS2 model and DGP model. For example, we analyse the dynamical evolution of the exponential potential model. And we find that the dynamical attractor caused by exponential potential can make the late time behavior insensitive to the initial condition that is helpful to avoid the fine tuning problem. In addition, we find the standard DGP model has a late-time self-acceleration solution and its equation of state w
本文着重研究一类近年来颇受关注的暗能量模型:胚世界暗能量模型。在胚世界宇宙学框架下,我们所生存的四维宇宙被认为是镶嵌在更高维的时空中,而引力相互作用可以在整个高维时空中传播。额外维度给宇宙学带来的效应目前无法被实验精确观测,因而也可能产生各种各样有趣和有意义的预言。这成为宇宙学家们为之不懈追求的动力之一。
在胚世界框架下建立的宇宙学暗能量模型也是丰富多样的,本文主要讨论其中最为流行的两类模型——RS2模型和DGP模型。全文结构如下:第一、二章简单回顾一下宇宙学几十年来的发展概况以及实验观测所取得的成果;第三章归纳宇宙学在暗能量理论方面取得的成果,并简单介绍几种最具代表性的暗能量模型;第四章将概括胚宇宙学的发展,从ADD模型的提出,到RS模型的引入,乃至现在倍受关注的DGP模型;第五、六章将详细分析RS2及DGP两种模型的宇宙学性质,尤其是对含指数势的这两种模型的演化行为进行了深入的动力学分析研究。我们观察到由指数势产生的动力学吸引子,可以使模型的后期行为对初始条件不敏感,从而有效的避免了精调问题。我们还发现标准DGP模型带来的晚期宇宙自加速膨胀,使其有效状态方程小于-1,而第二类DGP模型在暗能量存在的情况下,通过引力修正使宇宙演化的有效状态方程穿越了-1,或趋于-1。这些结果都非常的有意思,能够很好的与今天的天体实验观测符合,给出加速膨胀的宇宙的解释,从而预测未来的宇宙演化。
Since Gamow proposed the explosion cosmology in the end of 1940s, people never stop studying on this new subject. With the development of the observation, we get more and more accurate data and realize that the universe is dominated by the dark energy and dark matter. Though the observation data shows the existence of the dark energy, we can’t observe it directly. The nature of the dark energy remains a mystery. Various models of dark energy have been proposed.
In this paper, we investigate some interesting models of dark energy, especially the brane scenario, in which our four dimensional universe is embedded in a higher dimensional spacetime where the gravitation can propagate in. Since the effect of the extradimension can’t be obtained by experiment exactly, the brane world models admit a much wider range of possibilities for dark energy. It forces the scientists to untie the mystery.
There are lots of dark energy models under the framework of brane world scenario. In this paper we will mainly discuss the Randall-Sundrum2 model and the Dvali-Gabadadze-Porrati model. The structure of the paper is arranged as follows:
In chapter1&2, I review the history of the universe and the result of observation;
In chapter3, I report the achievement in theoretical study of dark energy,emphasizing on several typical models;
In chapter 4, I study the development of the brane scenario and summarize several major brane models;
The main work of this thesis is in chapter 5&6 in which I describe the property of RS2 model and DGP model. For example, we analyse the dynamical evolution of the exponential potential model. And we find that the dynamical attractor caused by exponential potential can make the late time behavior insensitive to the initial condition that is helpful to avoid the fine tuning problem. In addition, we find the standard DGP model has a late-time self-acceleration solution and its equation of state w
引文
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[3]A.D.Linde,Phys.Lett.B108(1982),389
[4]A.Albrecht and J.Steinhardt,Phys.Rev.Lett.48,(1982),1220
[5]俞允强,《物理宇宙学讲义》(第二版),北京大学出版社(2006)
[6]Edmund J.Copeland et al., Int.J.Mod.Phys.D15(2006) 1753-1936
[7]P.J.E.Peebles , Rev.Mod.Phys.75(2003) 559-606
[8]C.L.Bennett et al.,Astrophs.J.,Suppl.Ser.148 (2003) 1
[9]C.B.Netterfield et al.,Astrophys.J.571(2002),604
[10]N.W.Halverson et al.,Astrophs.J.568(2002),38
[11]M.Tegmark et al., [SDSS Collaboration] ,Phys.Rev.D 69,(2004),103501
[12]U.Seljak et al.,Phys.Rev.D71(2005)103515
[13]J.L.Tonry,Astrophys.J.524,(2003),1
[14]J.M.Ostriker and P.J.Steinhardt,Nature 377,(1995),600
[15]S.Weinberg ,Mod.Phys.61,(1989),1
[16]P.J.E.Peebles,B.Ratra,Rev.Mod.Phys.75,(2003)
[17] T.Padmanabhan,Phys.Rep.380,(2003)
[18] Li.X.Z and Hao.J.G, Phys.Rev.D69,(2004),107303 Li.X.Z,Hao.J.G and Liu.D.J, Int,J.Mod.Phys.A18(2003),5921
[19]R.R.Caldwell,Phys.Lett.b545(2002),23
[20]Hao.J.G and Li.X.Z,Phys.Rev.D68,(2003),043501 Liu.D.J and Li.X.Z,Phys.Rev.D68(2003),067301
[21]Li.X.Z and Zhai.X.H,Phys.Rev.D67(2003),067501
[22]Li.X.Z,et al,J.Shanghai Normal Univ.(Natural Sciences),Vol.33(4),(2004),29
[23]M.C.Bento et al, Phys.Rev.D67(2003),063003
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[28]G.W.Gibbons,Phys.Lett.B537(2002),1
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[33]T.Chiba,Phys.Lett.B 575(2003),1
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[35]L.Randall and R.Sundrum,Phys.Rev.Lett.83,(1999),4690 L.Randall and R.Sundrum,Phys.Rev.Lett.83,(1999),3370
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[38]N.Arkani-Hamed,S.Dimopoulos and G.Dvali,Phys.Lett.B429(1998 ),263 N.Arkani-Hamed,S.Dimopoulos and G.Dvali,Phys.Lett.B436(1998 ),257
[39]G.R.Dvali,G.Gabadadze and M.Porrati.,Phys.Lett.B.485(2000),208
[40] G.R.Dvali et al.,Phys.Rev.D64(2001) 084004 G.R.Dvali et al.,Phys.Rev.D65(2002) 024031
[41]Cedric.Deffayet,Phys.Lett.B502(2001)199-208
[42]V.Sahni and y.Shatanov,JCAP 0311(2003),014
[43]A.Lue and G.D.Starkman, Phys.Rev.D70 (2004),101501(R)
[44]S.M.Carroll et al, Phys.Rev[J].2004.D70,043528
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[46]Ruth.Lazkoz et al,Phys.Rev.D74(2006),083510
[47]Zhang.H.S and Zhu.Z.H, Phys.Rev.D75(2007),023510
[48]S.Perlmutter et al.,Aatrophys.J.517(1999),565
[49]A.G..Riess et al.,Astron.J.116(1998),1009 A.G..Riess et al.,Astron.J.117(1999),707
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