Rees--Sciama Effect and Impact of Foreground Structures on Galaxy
  Redshifts
  We estimate the Rees--Sciama (RS) effect of super structures on the cosmic
microwave background (CMB) temperature fluctuations and identify a related
effect on galaxy redshifts. By numerically solving the geodesic equation, we
find that both superclusters and supervoids can decrease the temperature of the
CMB by several micro Kelvin in the central region and increase the temperature
slightly in the surrounding area due to the RS effect. The two components of
the RS effect, redshift and gravitational time delay, largely cancel each
other, leaving an equivalent but much smaller effect on the CMB photons that
started out at the same time from the distorted last scattering surface. For
galaxies, the time delay effect is separable from the redshift effect, and the
slight change to the redshift induced by super structures can be at the percent
level of large-scale rms bulk velocities, which might only be detected
statistically. On much smaller scales, a tiny redshift difference between two
images of a strongly lensed source should exist in general, which is related to
the Hubble expansion rate at the source redshift. However, as Loeb (1998)
pointed out, observational issues and the proper motion of the structure would
make such a measurement impossible.
