Null geodesic congruences, gravitational lensing and CMB intensity
  profile
  It is known that the Cosmic Microwave Background (CMB) temperature
fluctuations are modified by gravitational lensing since the angular positions
of photons are altered by the metric perturbations. We reconsider this effect
in the context of geodesic deviation on a perturbed Friedmann-Robertson-Walker
(FRW) spacetime with scalar and tensor modes. We first give an alternative
derivation of the Sachs-Wolfe effect by using the solutions of the null
geodesic equation. Then, we determine the two-dimensional induced metric on the
transverse cross section of the null geodesic congruence corresponding to a
beam of photons after decoupling. This metric, whose variation along the
congruence can be decomposed as expansion and shear, is shown to produce a
nontrivial intensity profile which can be characterized by three variables
analogous to the Stokes parameters of the polarization tensor.
