主要研究了修改引力论在非线性尺度上的表现.现在已经存在很多修改引力论的模型,如f(R),DGP,Mond等,但是在工作中并没有使用别人已经提出的修改引力论方法,因为首先不可能去对所有的修改引力论模型都进行研究;其次重点研究的是修改引力对于宇宙中的物质分布在非线性尺度上的影响,而各种修改引力论对于物质聚集的影响是相似的,都可以通过一个参数表达出来.因此笔者提出一种修改引力论的方法,引进了一个简单参数ζ.这个参Geff/G数ζ定义为-φ/ψ,这里Geff是有效牛顿常数,G是牛顿常数,φ和ψ则是时空度规的标量扰动方程中的两个势.这个ζ参数在广义相对论的基础上修改了物质粒子受到的加速度,加大或者减小这个参数会相应地改变物质粒子的加速度,进而会加快或者减慢大尺度结构的形成.这种对大尺度结构在线性尺度上的影响可以通过理论计算得到,但是大尺度结构的非线性增长无法通过理论计算得出,现在只有借助已经发展得比较成熟的数值模拟方法来研究这个广问题.该文修改了现在已经比较成熟的数值模拟程序GADGET-2,加入了ζ参数.在进行数值模拟之前,首先检验了数值模拟的质量分辨率、模拟尺度,以及初始红移对最终物质功率谱的影响,并且证实修改后的GADGET-2程序是正确的.设定不同ζ参数的值,ζ=0.8,0.9,1.0,1.1,1.2,1.5,这里ζ=1.0对应标准宇宙学,然后对每个ζ值运行了一组数值模拟.%This thesis mainly focuses on the effects of modified gravity (MG) model on nonlinear scale. There are many different modified gravity models at present, e.g. f(R), DGP, MOND, etc.We do not use other's model directly, because most of those modified gravity models have similar effect on the matter distribution. Here, we proposed a different model. This model is based on a new parameter ζ, which is defined as Geff/G/(-φΨ), where Geff is effective Newton's constant, Gis Newton's constant, and φ, Ψ are the two potentials in the scalar perturbation of the space time metric. This parameter mainly changes the particles' acceleration. So, it will increase or decrease the structure formation. The linear effect can be calculated through theory. However,simulation is the only way which we can get the nonlinear evolution of large scale structure.We modified the mature simulation program-GADGET-2, and added ζ parameter in it. Before the simulation begins, we checked the effects of the mass resolution, simulation box, and initial redshift, and we also checked the correctness of the modified program. We set different value of ζ,ζ= 0.8, 0.9, 1.0, 1.1, 1.2,1.5, and begin our simulation.In order to reduce the numerical effect, and to show the modified gravity effects on non-linear scale, we do not use power spectrum directly. Instead, we set different output redshift for ζ, and make sure that different ζ have the same linear power spectrum at its output redshift. We used ζ =ζ≠ 1.0/(ζ=1.0) at last.After performing a series of simulations with cosmological scale, and using our wavelets method to calculate power spectrum, we are able to precisely study this MG method on nonlinear scale.We specify the output of the snapshot when different ζ have the same linear power spectrum.Those sets of output make an easy comparison on nonlinear scale. We find that the nonlinear power spectrum is the same as the linear power spectrum or increase with larger ζ. This result denies the assumption of HKLM, so, all the all-known power spectrum fitting formula which are based on this assumption are not suited for MG models. Further, based on our model, we come up with a new fitting formula, which is not an extension of those power spectrum. The new modified gravity non-linear power spectrum fitting formula is based on non-linear power spectrum, and it can be got through several parameters with a 5％ accuracy. We will continue to work on the peculiar velocity power spectrum of this MG simulations, halo mass function and the properties of halo. Those works will provide a guide for investigating those MC models on observations.
展开▼
