CMB observations in LTB universes: Part II: the kSZ effect in an LTB universe

TL;DR

This paper investigates the kSZ effect in an LTB universe model that mimics the standard cosmology's distance-redshift relation, finding that large inhomogeneities or isocurvature perturbations are needed to match observations.

Contribution

It provides a detailed calculation of the kSZ effect in an LTB universe with a void, highlighting the challenges in reconciling such models with observational data.

Findings

Dipole anisotropy dominates CMB temperature fluctuations in the model.

Large drift velocities are required if assuming adiabatic initial conditions.

Introducing isocurvature perturbations can relax observational constraints.

Abstract

We study the kinematic Sunyaev-Zel'dovich (kSZ) effect in a Lem\^itre-Tolman-Bondi (LTB) universe model whose distance-redshift relation agrees with that of the concordance $\Lambda$CDM model at redshifts $z\lesssim2$. This LTB universe model has a void with size comparable to the Hubble horizon scale. We first determine the decoupling epoch in this LTB universe model by an approximate analytical condition under a few simplified assumptions on the physical quantities at that epoch. Then we calculate the cosmic microwave background (CMB) anisotropy observed in the rest frame of clusters of galaxies which are assumed to be at rest in the spatial comoving coordinates of the LTB universe model. We find that the obtained temperature anisotropies are dominated by dipole, although there may exist higher multi-poles in general. We may interpret this dipole anisotropy as the drift velocity of a cluster of galaxies relative to the CMB rest frame. Hence it gives rise to the kSZ effect. We calculate this effect and compare it with observational data. We find that if we assume the conventional adiabatic perturbation scenario at the time of decoupling, the drift velocity of clusters of galaxies becomes unacceptably large. Conversely, this observational constraint may be relaxed by introducing a non-adiabatic (i.e., primordially isocurvature) component of inhomogeneities at the time of decoupling. However, our result indicates that the necessary isocurvature perturbation amplitude is very large.