CMB seen through random Swiss Cheese

TL;DR

This paper investigates how a Swiss Cheese cosmological model with randomly arranged Lemaître--Tolman--Bondi holes affects CMB temperature, shear, and distance measurements, providing new insights into their systematic shifts and power spectra.

Contribution

It introduces the first calculation of shear effects in Swiss Cheese models and compares the robustness of distance and shear power spectra against perturbation theory.

Findings

CMB temperature power spectrum is much smaller than the linear ISW spectrum.

Distance and shear power spectra are consistent with perturbation theory.

No significant mean shift in the angular diameter distance was found.

Abstract

We consider a Swiss Cheese model with a random arrangement of Lema\^itre--Tolman--Bondi holes in $\Lambda$CDM cheese. We study two kinds of holes with radius $r_b=50 h^{-1}$Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB. We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra. In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95\% limit $|\Delta D_A/\bar{D}_A|\lesssim10^{-4}$. We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. The closed case is consistent with this at 1$\sigma$, whereas in the open case the probability is only 1.4%.