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

Understand

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.