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