Formation of voids in the Universe within the Lemaître–Tolman model

We develop models of void formation starting from a small initial fluctuation at recombination and growing to a realistic present-day density profile in agreement with observations of voids. The model construction is an extension of previously developed algorithms for finding a Lemaître–Tolman metric that evolves between two profiles of either density or velocity specified at two times. Of the four profiles of concern (those of density and velocity at recombination and at the present day), two can be specified and the other two follow from the derived model.
We find that, in order to reproduce the present-day void density profiles, the initial velocity profile is more important than the initial density profile.
Extrapolation of current cosmic microwave background (CMB) observations to the scales relevant to protovoids is very uncertain. Even so, we find that it is very difficult to make both the initial density and velocity fluctuation amplitudes small enough and still obtain a realistic void by today.     

Full-sky correlations of peaks in the microwave background

We compute precise predictions for the two-point correlation function of local maxima (or minima) in the temperature of the microwave background, under the assumption that it is a random Gaussian field. For a given power spectrum and peak threshold there are no adjustable parameters, and since this analysis does not make the small-angle approximation of Heavens & Sheth, it is essentially complete. We find oscillatory features which are absent in the temperature autocorrelation function, and we also find that the small-angle approximation to the peak–peak correlation function is accurate to better than 0.01 on all scales. These high-precision predictions can form the basis of a sensitive test of the Gaussian hypothesis with upcoming all-sky microwave background experiments MAP and Planck , affording a thorough test of the inflationary theory of the early Universe. To illustrate the effectiveness of the technique, we apply it to simulated maps of the microwave sky arising from the cosmic string model of structure formation, and compare the two-point correlation function of peaks with the bispectrum as a non-Gaussian discriminant. We also show how peak statistics can be a valuable tool in assessing and statistically removing contamination of the map by foreground point sources.     

The correlation of peaks in the microwave background

We present accurate small-angle predictions of the correlation function of hotspots in the microwave background radiation for Gaussian theories such as those predicted in most inflation models. The correlation function of peaks above a certain threshold depends only on the threshold and the power spectrum of temperature fluctuations. Since these are both potentially observable quantities in a microwave background map, there are no adjustable parameters in the predictions. These correlations should therefore provide a powerful test of the Gaussian hypothesis, and provide a useful discriminant between inflation and topological defect models such as the cosmic string model. The correlations have a number of oscillatory features, which should be detectable at high signal-to-noise ratio with future satellite experiments such as MAP and Planck .     

Global fits for the spectral index of the cosmological curvature perturbation

Best-fitting values of the spectral index of the curvature perturbation are presented, assuming the ΛCDM cosmology. Apart from the spectral index, the parameters are the Hubble parameter, the total matter density and the baryon density. The data points are intended to represent all measurements that are likely to affect the result significantly. The cosmic microwave anisotropy is represented by the COBE normalization, and heights of the first and second peaks are given by the latest Boomerang and Maxima data. The slope of the galaxy correlation function and the matter density contrast on the 8  h ⁻¹ Mpc scale are each represented by a data point, as are the expected values of the Hubble parameter and matter density. The 'low-deuterium' nucleosynthesis value of the baryon density provides a final data point, the fit giving a value higher by about one standard deviation. The reionization epoch is calculated from the model by assuming that it corresponds to the collapse of a fraction f ≳10⁻⁴ of matter. We consider the case of a scale-independent spectral index, and also the scale-dependent spectral index predicted by running mass models of inflation. In the former case, the result is compared with the prediction of models of inflation based on effective field theory, in which the field value is small on the Planck scale. A detailed comparison is made with other fits, and other approaches to the comparison with theory.     

Estimating non-Gaussianity in the microwave background

The bispectrum of the microwave background sky is a possible discriminator between inflationary and defect models of structure formation in the Universe. The bispectrum, which is the analogue of the temperature three-point correlation function in harmonic space, is zero for most inflationary models, but non-zero for non-Gaussian models. The expected departures from zero are small, and easily masked by noise, so it is important to be able to estimate the bispectrum coefficients as accurately as possible, and to know the errors and correlations between the estimates so that they may be used in combination as a diagnostic to rule out non-Gaussian models. This paper presents a method for estimating in an unbiased way the bispectrum from a microwave background map in the near-Gaussian limit. The method is optimal, in the sense that no other method can have smaller error bars, and, in addition, the covariances between the bispectrum estimates are calculated explicitly. The method deals automatically with partial sky coverage and arbitrary noise correlations without modification. A preliminary application to the Cosmic Background Explorer 4-yr data set shows no evidence for non-Gaussian behaviour.     

On the APM power spectrum and the CMB anisotropy: evidence for a phase transition during inflation?

Adams et al. have noted that according to our current understanding of the unification of fundamental interactions, there should have been phase transitions associated with spontaneous symmetry breaking during the inflationary era. This may have resulted in the breaking of scale-invariance of the primordial density perturbation for brief periods. A possible such feature was identified in the power spectrum of galaxy clustering in the automated plate measurement (APM) survey at the scale k  ∼ 0.1  h  Mpc ^− 1 and it was shown that the secondary acoustic peaks in the power spectrum of the cosmic microwave background (CMB) anisotropy should consequently be suppressed. We demonstrate that this prediction is confirmed by the recent Boomerang and Maxima observations, which favour a step-like spectral feature in the range k  ∼ (0.06–0.6)  h  Mpc ^− 1 , independently of the similar previous indication from the APM data. Such a spectral break enables an excellent fit to both APM and CMB data with a baryon density consistent with the big bang nucleosynthesis (BBN) value. It also allows the possibility of a matter-dominated universe with zero cosmological constant, which we show can now account for even the evolution of the abundance of rich clusters.     

宇宙微波背景辐射极化的近似解析公式

在宇宙早期的退耦过程中，光子与电子发生Thompson散射．光子气体空间分布的各向异性通过Thompson散射而产生宇宙微波背景辐射的极化，并为最近WMAP观测到．从光子气体的Boltzmann方程出发，采用一般的光深函数，分别积分给出原初密度扰动和残余引力波产生的微波背景辐射极化的近似解析解，结果适用于一般的复合过程．密度扰动FS所产生极化的近似解析解为βS≌-CFs(Td)ΔTd，其中Td和△Td分别为退耦时刻和退耦宽度，系数C≌(0．08—0．12)，明显依赖于复合模型．残余引力波扰动FT产生极化的积分稍微复杂，在长波近似下我们对原初扰动按波数进行幂级数展开，保留到两项FT≌FT^(1) FT(2)，分别积分，给出近似解析解βT≌-[CFT^(1)(Td) DFT^(2)(Td)]ΔTd.第一项的极化与密度扰动类似，结论也相同；但第二项的系数D≌(0．22—0．32)，远大于系数C，我们的近似解析解有助于理解背景辐射的温度一极化交叉关联和检测残余引力波对背景辐射各向异性的贡献．     

The cosmic microwave background for a nearly flat compact hyperbolic universe

The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy and an extra spatially constant dark energy X -component are considered. The general solution of the Friedmann equation for the cosmic scalefactor a ( η ) is given for the four-component models in terms of the Weierstrass ℘-function. The lower parts of the angular power spectra C _l of the CMB anisotropy are computed for nearly flat models with Ω_tot≤0.95. It is shown that the particular compact fundamental cell that is considered in this paper leads to a suppression in C _l for l ≲10 and Ω_tot≲0.9.     

Constraints on large-scale inhomogeneities from WMAP5 and SDSS: confrontation with recent observations

Measurements of the Type Ia supernovae Hubble diagram which suggest that the Universe is accelerating due to the effect of dark energy may be biased because we are located in a 200–300 Mpc underdense 'void' which is expanding 20–30 per cent faster than the average rate. With the smaller global Hubble parameter, the Wilkinson Microwave Anisotropy Probe 5 data on cosmic microwave background (CMB) anisotropies can be fitted without requiring dark energy if there is some excess power in the spectrum of primordial perturbations on 100 Mpc scales. The Sloan Digital Sky Survey (SDSS) data on galaxy clustering can also be fitted if there is a small component of hot dark matter in the form of 0.5 eV mass neutrinos. We show however that if the primordial fluctuations are Gaussian, the expected variance of the Hubble parameter and the matter density are far too small to allow such a large local void. Nevertheless, many such large voids have been identified in the SDSS Luminous Red Galaxy survey in a search for the late integrated Sachs–Wolfe effect due to dark energy. The observed CMB temperature decrements imply that they are nearly empty, thus these real voids too are in gross conflict with the concordance Λ cold dark matter model. The recently observed high peculiar velocity flow presents another challenge for the model. Therefore, whether a large local void actually exists must be tested through observations and cannot be dismissed a priori.     

On the importance of high-redshift intergalactic voids

We investigate the properties of 1D flux 'voids' (connected regions in the flux distribution above the mean-flux level) by comparing hydrodynamical simulations of large cosmological volumes with a set of observed high-resolution spectra at z ∼ 2. After addressing the effects of box size and resolution, we study how the void distribution changes when the most significant cosmological and astrophysical parameters are varied. We find that the void distribution in the flux is in excellent agreement with predictions of the standard Λcold dark matter (ΛCDM) cosmology, which also fits other flux statistics remarkably well. We then model the relation between flux voids and the corresponding 1D gas-density field along the line of sight and make a preliminary attempt to connect the 1D properties of the gas-density field to the 3D dark matter distribution at the same redshift. This provides a framework that allows statistical interpretations of the void population at high redshift using observed quasar spectra, and eventually it will enable linking the void properties of the high-redshift universe with those at lower redshifts, which are better known.