The Szekeres Swiss Cheese model and the CMB observations

TL;DR

This paper applies the exact Szekeres Swiss Cheese model to study the impact of inhomogeneous matter distribution on CMB observations, revealing that small-scale inhomogeneities have minor effects, but large local inhomogeneities could explain some anomalies.

Contribution

It introduces the use of the inhomogeneous, non-symmetrical Szekeres model for realistic analysis of light propagation effects on CMB, beyond linear perturbation approaches.

Findings

Small-scale inhomogeneities induce minor temperature fluctuations.

Large local inhomogeneities can cause significant temperature fluctuations.

These effects may explain low multipole anomalies in the CMB spectrum.

Abstract

This paper presents the application of the Szekeres Swiss Cheese model to the analysis of observations of the cosmic microwave background (CMB) radiation. The impact of inhomogeneous matter distribution on the CMB observations is in most cases studied within the linear perturbations of the Friedmann model. However, since the density contrast and the Weyl curvature within the cosmic structures are large, this issue is worth studying using another approach. The Szekeres model is an inhomogeneous, non-symmetrical and exact solution of the Einstein equations. In this model, light propagation and matter evolution can be exactly calculated, without such approximations as small amplitude of the density contrast. This allows to examine in more realistic manner the contribution of the light propagation effect to the measured CMB temperature fluctuations. The results of such analysis show that small-scale, non-linear inhomogeneities induce, via Rees-Sciama effect, temperature fluctuations of amplitude $10^{-7} - 10^{-5}$ on angular scale $\theta< 0.24^{\circ}$ ($\ell > 750$). This is still much smaller than the measured temperature fluctuations on this angular scale.However, local and uncompensated inhomogeneities can induce temperature fluctuations of amplitude as large as $10^{-3}$, and thus can be responsible the low multipoles anomalies observed in the angular CMB power spectrum.