Cosmic microwave background anisotropy: deviations from Gaussianity caused by non-linear gravity

Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N-body simulations - in aCDM cosmology - are used to simulate the strongly non-linear evolution of cosmological structures. It is proved that these simulations can be combined with the potential approximation to calculate the statistical moments of the CMB anisotropies produced by non-linear gravity. Some of these moments are computed and the resulting values are different from those corresponding to Gaussianity.

The great attractor and the COBE quadrupole

A nonlinear model for the Great Attractor is built. It is based on the Tolman-Bondi solution of the Einstein equations. The angular temperature distribution of the Cosmic Microwave Background produced by the Great Attractor is numerically obtained. Several realizations of the Great Attractor are studied. In all the cases, the distance from the Great Attractor to the Local Group is ≈ 43h−1 Mpc, the density contrast reduces to a half of the central value at a radius of 9h−1 Mpc ⪯ Rc ⪯ 14h−1 Mpc, and the dipole due to the infall towards the inhomogeneity center is 1.33 × 10−3 ⪯ D ⪯ 1.8 × 10−3. A complete arbitrary background is assumed; the density parameter, Σ and the reduced Hubble constant,…

Estimating small angular scale CMB anisotropy with high resolution N-body simulations: weak lensing

We estimate the impact of weak lensing by strongly nonlinear cosmological structures on the cosmic microwave background. Accurate calculation of large $\ell$ multipoles requires N-body simulations and ray-tracing schemes with both high spatial and temporal resolution. To this end we have developed a new code that combines a gravitational Adaptive Particle-Particle, Particle-Mesh (AP3M) solver with a weak lensing evaluation routine. The lensing deviations are evaluated while structure evolves during the simulation so that all evolution steps--rather than just a few outputs--are used in the lensing computations. The new code also includes a ray-tracing procedure that avoids periodicity effect…

On the microwave background anisotropy produced by big voids in open universes

The Tolman-Bondi solution of the Einstein equations is used in order to model the time evolution of the void observed in Bo\"otes. The present density contrast of the central region ($\sim -0.75$) and its radius ($\sim 30h^{-1} \ Mpc$) are fixed, while the density parameter of the Universe, the amplitude of the density contrast inside the void wall, the width of this wall and the distance from the void centre to the Local Group are appropriately varied. The microwave background anisotropy produced by Bo\"otes-like voids is estimated for a significant set of locations. All the voids are placed far from the last scattering surface. It is shown that the anisotropy generated by these voids stro…

ESTIMATING SMALL ANGULAR SCALE COSMIC MICROWAVE BACKGROUND ANISOTROPY WITH HIGH-RESOLUTIONN-BODY SIMULATIONS: WEAK LENSING

We estimate the impact of weak lensing by strongly nonlinear cosmological structures on the cosmic microwave background. Accurate calculation of large l multipoles requires N-body simulations and ray-tracing schemes with both high spatial and temporal resolution. To this end, we have developed a new code that combines a gravitational Adaptive Particle-Particle, Particle-Mesh solver with a weak-lensing evaluation routine. The lensing deviations are evaluated while structure evolves during the simulation so that all evolution steps—rather than just a few outputs—are used in the lensing computations. The new code also includes a ray-tracing procedure that avoids periodicity effects in a univer…

Looking for the imprints of nonlinear structures on the cosmic microwave background

Abstract Many authors have estimated the anisotropies produced by one isolated cosmological non-linear inhomogeneity. This paper is an updated review about these estimates. The main methods used in order to deal with this problem are described. The limitations of these methods are analyzed. Results appear to be particularly interesting in the open non-linear case, in which a general treatment of the anisotropies produced by inhomogeneity distributions is very troublesome. The effects produced by very big structures such as the Great Attractor and the Bootes Void are studied in detail. Some generalities about the origin, detection and features of the Cosmic Microwave Background anisotropies …

The imprints of the Great Attractor and the Virgo cluster on the microwave background

A fully non-linear model based on the Tolman-Bondi solution of the Einstein equations is used to describe the Great Attractor and the Virgo cluster. The background is a Friedmann-Robertson-Walker universe, and the inhomogeneity develops from physically motivated initial profiles of the energy density and the peculiar velocity. Accurate numerical integrations of the field equations of the null geodesics are carried out, and thus the angular temperature distribution of the microwave background produced by the chosen overdensities is found. The observer is located in the Local Group. The quadrupole Q produced by each overdensity is computed and divided into two parts: the relativistic Doppler …

Deconvolving the Beam in Small Angular Scale CMB Experiments

This paper is concerned with experiments which measure CMB anisotropies on small angular scales. A certain coverage, a beam structure and a level of uncorrelated noise define each experiment. We focus our atention on the reversion of the beam average. In each experiment, we look for the best pixelization for reversion, namely, for the pixelization that -after reversion- leads to good maps containing right spectra for the most wide range of angular scales. Squared pixels having different sizes "smaller" than the beam radius are considered. For a given size, the following question arises: How well can we assign a temperature to each pixel? Various mathematical methods are used to show that, i…

On the Rees-Sciama effect: maps and statistics

Small maps of the Rees-Sciama (RS) effect are simulated by using an appropriate N-body code and a certain ray-tracing procedure. A method designed for the statistical analysis of cosmic microwave background (CMB) maps is applied to study the resulting simulations. These techniques, recently proposed --by our team-- to consider lens deformations of the CMB, are adapted to deal with the RS effect. This effect and the deviations from Gaussianity associated to it seem to be too small to be detected in the near future. This conclusion follows from our estimation of both the RS angular power spectrum and the RS reduced n-direction correlation functions for n<7.

Great Attractor-like structures and large-scale anisotropy

On the estimation and detection of the Rees Sciama effect

Maps of the Rees–Sciama (RS) effect are simulated using the parallel N-body code, hydra, and a run-time ray-tracing procedure. A method designed for the analysis of small, square cosmic microwave background (CMB) maps is applied to our RS maps. Each of these techniques has been tested and successfully applied in previous papers. Within a range of angular scales, our estimate of the RS angular power spectrum due to variations in the peculiar gravitational potential on scales smaller than 42/h megaparsecs is shown to be robust. An exhaustive study of the redshifts and spatial scales relevant for the production of RS anisotropy is developed for the first time. Results from this study demonstra…

Non-circular rotating beams and CMB experiments

This paper is concerned with small angular scale experiments for the observation of cosmic microwave background anisotropies. In the absence of beam, the effects of partial coverage and pixelisation are disentangled and analyzed (using simulations). Then, appropriate maps involving the CMB signal plus the synchrotron and dust emissions from the Milky Way are simulated, and an asymmetric beam --which turns following different strategies-- is used to smooth the simulated maps. An associated circular beam is defined to estimate the deviations in the angular power spectrum produced by beam asymmetry without rotation and, afterwards, the deviations due to beam rotation are calculated. For a cert…

Learning from observations of the microwave background at small angular scales

In this paper, we focus our attention on the following question: How well can we recover the power spectrum of the cosmic microwave background from the maps of a given experiment?. Each experiment is described by a a pixelization scale, a beam size, a noise level and a sky coverage. We use accurate numerical simulations of the microwave sky and a cold dark matter model for structure formation in the universe. Angular scales smaller than those of previous simulations are included. The spectrum obtained from the simulated maps is appropriately compared with the theoretical one. Relative deviations between these spectra are estimated. Various contributions to these deviations are analyzed. The…