Galaxy Clusters as mirrors of the distant Universe. Implications for the
  kSZ and ISW effects
  It is well known that Thomson scattering of CMB photons in galaxy clusters
introduces new anisotropies in the CMB radiation field, but however little
attention is payed to the fraction of CMB photons that are scattered off the
line of sight, causing a slight blurring of the CMB anisotropies present at the
moment of scattering. In this work we study this {\it blurring} effect, and
find that it has a non-negligible impact on estimations of the kinetic
Sunyaev-Zel'dovich (kSZ) effect: it induces a 10% correction in 20-40% of the
clusters/groups, and a 100% correction in $\sim 5$% of the clusters in an ideal
(noiseless) experiment. We explore the possibility of using this blurring term
to probe the CMB anisotropy field at different epochs in our Universe. In
particular, we study the required precision in the removal of the kSZ that
enables detecting the blurring term $-\tau_T \delta T / T_0$ in galaxy cluster
populations placed at different redshift shells. By mapping this term in those
shells, we would provide a tomographic probe for the growth of the Integrated
Sachs Wolfe effect (ISW) during the late evolutionary stages of the Universe.
We find that the required precision of the cluster peculiar velocity removal is
of the order of 100 -- 200 km s$^{-1}$ in the redshift range 0.2 -- 0.8, after
assuming that all clusters more massive than 10$^{14}$ h$^{-1}$ M$_{\odot}$ are
observable. These errors are comparable to the total expected linear line of
sight velocity dispersion for clusters in WMAPV cosmogony, and correspond to a
residual level of roughly 900 -- 1800 $\tau_T \mu$K per cluster, including all
types of contaminants and systematics. Were this precision requirement
achieved, then independent constraints on the intrinsic cosmological dipole
would be simultaneously provided.
