初始谱指数为-1的非线性重谱(Bispectrum)

重谱即傅立叶空间的三点相关函数，是研究由引力不稳定性产生的大尺度结构的最低非高斯阶统计性质．在傅立叶空间中，发现二维和三维空间的统计性质是等价的，相对三维快速傅立叶，二维快速傅立叶变换可以节省很多计算机资源．结合二维和三维的快速傅立叶变换，利用高精度的初始谱指数为-1的N体数值模拟，测量了从弱线性区域到强非线性区域的重谱．在测量过程中，考虑并严格校正了作用于功率谱和重谱上的数值效应，如离散效应（particle discreteness）、软化因子（force softening）、模拟盒子的大小、混淆效应（alias effect）．发现约化重谱即使在强非线性区域仍然依赖于三角形的形状和尺度，并随着波数的增加而增加，这和前人的假设完全不同．在测量结果的基础上，拟合了重谱的一个适用于初始谱指数为-1的宇宙学模型的经验公式．     

宇宙中大尺度非线性结构

宇宙物质在大尺度上成团是宇宙学的基本问题.本文综述了金斯理论和泽利多维奇近似,指出:双成分自引力系统的非线性相互作用的动力学描述是大尺度成团的现代研究课题. 详述了过去在这个课题方面被我们获得的结果.表明:自引力系统的结构可由一组非线性藕合方程描写:扰动场能塌缩并形成类薄饼结构.在宇宙条件下,我们得到了星系团、超团和巨洞的特征尺度.     

宇宙大尺度结构数值模拟的研究进展

宇宙的结构是由初始密度扰动发展而成的。在引力和宇宙膨胀的作用下,初始密度扰动不断增长,经过线性和非线性阶段,逐渐演化为现今的宇宙结构。在一个给定的宇宙学模型下,可以用一系列动力学方程来描述宇宙中暗物质和重子物质的运动及演化历史。在过去的几十年间,随着算法的完善和计算机技术的发展,从最初几十个粒子的纯引力模拟到1010个粒子在秒差距量级的多体加流体动力学模拟,大量不同的数值模拟技术被用来研究宇宙结构的形成和演化。在这个过程中,数值模拟的分辨率和精度不断提高,模型中对重子物质物理过程的描述也越来越完善。这些模拟技术与观测结果相结合,使人们对宇宙的大尺度结构以及星系团的形成和演化有了更深刻的理解,也在一定程度上影响了观测的发展方向和设备研发。不同数值模拟结果在纯引力研究方面得到了较好的统一,但不同的星系模型使得流体模拟的结果存在较大的差异。     

ISW效应对Yukawa引力势的检验

该文利用Integrated Sachs-Wolfe(ISW)效应探测宇宙大尺度引力势随时间的变化速率,从而能够在宇宙学尺度上检验引力的性质.以Yukawa引力势为例,探讨了利用ISW效应检验引力性质的能力.计算表明,ISW效应对引力的性质很敏感,通过与宇宙微波背景辐射实验WMAP五年的观测结果相比较,发现相对于牛顿常数,等效牛顿常数在宇宙学尺度上最多只有约2%的改变.     

重构Ly-α线丛的功率谱约束对数正态(LN)模型参数

选择3个类星体Keck观测样本,使用Gauss化方法重构宇宙质量密度扰动场,并计算相应的小波功率谱．同时,设定对数正态(LN)模型中的形状因子Γ和平滑因子r为自由参数,并通过数值模拟生成模拟样本,与观测样本的统计结果做拟合,来确定Γ和r．结合观测的辐射流量功率谱和数值模拟的结果可以唯一确定Γ的值,最后得到Γ≈0．50,r≈0．0g．类星体的辐射流量是非Gauss的,使用传统的Gauss化方法无法消除非Gauss特征．但是观测样本和数值模拟样本的偏斜谱、峰度谱以及尺度-尺度相关等非Gauss特征的表征量在研究的尺度(>100kpc)上表现一致,这就支持了拟合的结果．     

宇宙在大尺度上是均匀的吗?

宇宙中的物质在大尺度上是均匀分布的,还是保持着分形分布的特点,成为近年来观测宇宙学中争论的一个热点。Ｐｉｅｔｒｏｎｅｒｏ等人认为直到目前观测到的最大尺度（≈１０００ｈ＾－１Ｍｐｃ）星系的分布仍保持Ｄ≈２的分形结构,而大多数坚持标准模型的宇宙学家都认为宇宙在大尺度上是均匀分布的。宇宙物质在大尺度上是否均匀分布,将由下一代的红移巡天的结果来判断。     

中国天文学家提出探索暗物质和暗能量的新方法

2008年7月,上海天文台张鹏杰研究员与国家天文台陈学雷研究员在《Physical Review D》上发表了题为（Type Ia supernovae as speed sensors at inter-mediate redshifts》的论文,阐述了通过Ia型超新星的视亮度变化来测量中等红移处宇宙大尺度本动速度,从而探索暗物质、暗能量和宇宙学尺度上引力性质的方法。     

利用地面深空激光测距检验相对论的引力时延

讨论了广义相对论的引力时延.根据Mini-ASTROD空间计划方案,利用地面深空激光测距来检验引力时延,给出了测量值与理论值直接比对的方案,并拟合出空间曲率参数γ的值.文中采用非同步的激光应答器、皮秒事件记数器等设备,可以提高测量的精度和稳定性.在地面站和行星探测器之间直接进行激光测距,不仅可以验证广义相对论的引力时延,而且还可以使γ的精度提高至少1～2个量级.这对于宇宙学和引力理论具有十分重要的意义.     

利用地面深空激光测距检验相对论的引力时延

讨论了广义相对论的引力时延。根据Mini－ASTROD空间计划方案，利用地面深空激光测距来检验引力时延，给出了测量值与理论值直接比对的方案，并拟合出空间曲率参数γ的值。文中采用非同步的激光应答器、皮秒事件记数器等设备，可以提高测量的精度和稳定性。在地面站和行星探测器之间直接进行激光测距，不仅可以验证广义相对论的引力时延，而且还可以使γ的精度提高至少1－2个量级。这对于宇宙学和引力理论具有十分重要的意义。     

基于深度学习的无碰撞引力N体数值模拟的可行性研究

提出了用深度神经网络代替快速傅里叶变换法求解无碰撞引力N体数值模拟方法PM-Tree(Partical Mesh Tree)中的势能,以提升PM-Tree方法的效率,验证深度学习方法加速无碰撞引力N体数值模拟的可行性.无碰撞引力N体数值模拟对研究星系、暗物质晕以及宇宙大尺度结构的形成和演化有重要意义.无碰撞引力N体数值...     

Peaks in the cosmological density field: sensitivity to initial power spectrum, redshift distortions and galaxy halo occupation

We investigate the number density of maxima in the cosmological galaxy density field smoothed with a filter as a probe of clustering. In previous work it has been shown that this statistic is closely related to the slope of the linear power spectrum, even when the directly measured power spectrum is non-linear. In the present paper we investigate the sensitivity of the peak number density to various models with differing power spectra, including rolling index models, cosmologies with massive neutrinos and different baryon densities. We find that rolling index models which have given an improved fit to CMB/LSS (cosmic microwave background/large scale structure) data yield a ∼10 per cent difference in peak density compared to the scale invariant case. Models with 0.3 eV neutrinos have effects of similar magnitude and it should be possible to constrain them with data from current galaxy redshift surveys. Baryon oscillations in the power spectrum also give rise to distinctive features in the peak density. These are preserved without modification when measured from the peak density in fully non-linear N -body simulations. Using the simulations, we also investigate how the peak density is modified in the presence of redshift distortions. Redshift distortions cause a suppression of the number of peaks, largely due to fingers of God overlapping in redshift space. We find that this effect can be modelled by using a modification of the input power spectrum. We also study the results when the simulation density field is traced by galaxies obtained by populating haloes with a halo occupation distribution consistent with observations. The peak number density is consistent with that in the dark matter for filter scales  >4  h ⁻¹ Mpc  , for which we find good agreement with the linear theory predictions. In a companion paper we analyse data from the 2dF Galaxy Redshift Survey.     

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

Non-linear redshift distortions: the two-point correlation function

We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ _s , the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ _s . While the deviations are insignificant for the monopole ξ ₀, the hexadecapole ξ ₄ exhibits large deviations from the linear predictions. For a COBE normalized     ,     cold dark matter (CDM) power spectrum, our results for ξ ₄ deviate from the linear predictions by a factor of two on the scale of ∼10  h ⁻¹ Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only     .
We also show that the commonly used phenomenological model, where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.     

Cluster formation and the Sunyaev–Zel'dovich power spectrum in modified gravity: the case of a phenomenologically extended DGP model

We investigate the effect of modified gravity on cluster abundance and the Sunyaev–Zel'dovich (SZ) angular power spectrum. Our modified gravity is based on a phenomenological extension of the Dvali–Gabadadze–Porrati model which includes two free parameters characterizing deviation from Λ cold dark matter cosmology. Assuming that Birkhoff's theorem gives a reasonable approximation, we study the spherical collapse model of structure formation and show that while the growth function changes to some extent, modified gravity gives rise to no significant change in the linear density contrast at collapse time. The growth function is enhanced in the so called normal branch, while in the 'self-accelerating' branch it is suppressed. The SZ angular power spectrum is computed in the normal branch, which allows us to put observational constraints on the parameters of the modified gravity model using small scale cosmic microwave background observation data.     

基于红移畸变测量宇宙结构增长率的进展

星系红移巡天的一个主要目标是依据光谱红移测距,详细刻画宇宙中星系的三维空间分布。由于星系本动速度的存在,红移空间的星系分布存在着严重畸变,在大小尺度上有着不同模式的各向同性偏离。通过对红移畸变的观测研究,人们可从中获取速度场的信息,因此,红移畸变已成为暗能量探测的重要探针之一,为检验宇宙学尺度上的引力模型提供帮助。当前星系红移巡天项目已经取得了非凡成功,为人们提供了详细的星系空间分布数据。人们据此测量了星系的相关函数和功率谱,提取了精确的红移畸变信号,并通过模型拟合限制出了一批不同红移处宇宙结构增长率的估值,为探索宇宙尺度的引力模式提供了数据支持。主要介绍红移畸变模型、星系红移巡天观测和宇宙结构增长率测量等研究进展。     

A DWT Power Spectrum Analysis of PSCz Galaxies

The power spectrum estimator based on the Discrete Wavelet Transformation (DWT) is applied to detect the clustering power in the IRAS Point Source Catalog Redshift Survey(PSCz). Comparison with mock samples extracted from N-body simulation shows that the DWT power spectrum estimator could provide a robust measurement of banded fluctuation power over a range of wavenumbers 0.1-2.0h Mpc^-1. We have fitted three typical CDM models (SCDM, TCDM and ACDM) using the Peacock-Dodds formula including non-linear evolution and redshift distortion. We find that, our results are in good agreement with other statistical measurements of the PSCz.     

HI fluctuations at large redshifts: II — the signal expected for the GMRT

For the GMRT, we calculate the expected signal from red-shifted HI emission at two frequency bands centered at 610 and 325 MHz. The study focuses on the visibility-visibility cross-correlations, proposed earlier as the optimal statistical estimator for detecting and analyzing this signal. These correlations directly probe the power spectrum of density fluctuations at the redshift where the radiation originated, and thereby provide a method for studying the large scale structures at large redshifts. We present detailed estimates of the correlations expected between the visibilities measured at different baselines and frequencies. Analytic fitting formulas representing the salient features of the expected signal are also provided. These will be useful in planning observations and deciding an optimal strategy for detecting this signal.     

The growth of correlations in the matter power spectrum

We find statistically significant correlations in the cosmological matter power spectrum over the full range of observable scales. While the correlations between individual modes are weak, the band-averaged power spectrum shows strong non-trivial correlations. The correlations are significant when the modes in either one or both bands are in the non-linear regime, and approach 100 per cent for pairs of bands in which all the modes are non-linear. The correlations are weaker, but not absent, when computed in redshift space. As estimates of the power spectrum from galaxy surveys require band-averaging, the correlations must be taken into account when comparing a measured power spectrum with theoretical models.     

Measurement of the baryonic acoustic oscillation scale in 21 cm intensity fluctuations during the reionization era

It has recently been suggested that the power spectrum of redshifted 21 cm fluctuations could be used to measure the scale of baryonic acoustic oscillations (BAOs) during the reionization era. The resulting measurements are potentially as precise as those offered by the next generation of galaxy redshift surveys at lower redshift. However, unlike galaxy redshift surveys, which in the linear regime are subject to a scale-independent galaxy bias, the growth of ionized regions during reionization is thought to introduce a strongly scale-dependent relationship between the 21 cm and mass power spectra. We use a seminumerical model for reionization to assess the impact of ionized regions on the precision and accuracy with which the BAO scale could be measured using redshifted 21 cm observations. For a model in which reionization is completed at   z ∼ 6  , we find that the constraints on the BAO scale are not systematically biased at   z ≳ 6.5  . In this scenario, and assuming the sensitivity attainable with a low-frequency array comprising 10 times the collecting area of the Murchison Widefield Array, the BAO scale could be measured to within 1.5 per cent in the range  6.5 ≲ z ≲ 7.5  .     

The power spectrum of the Lyman-α clouds

We investigate the clustering properties of 13 QSO lines of sight in flat space, with average redshifts from z ≈2 to 4. We estimate the 1D power spectrum and the integral density of neighbours, and discuss their variation with respect to redshift and column density. We compare the results with standard CDM models, and estimate the power spectrum of Lyman- α clustering as a function of both redshift and column density. We find that (a) there is no significant periodicity or characteristic scale; (b) the clustering depends on both column density and redshift; (c) the clustering increases linearly only if at the same time the H  i column density decreases strongly with redshift. The results remain qualitatively the same, assuming an open cosmological model.