Lensing

Gravitational lensing is normally said to introduce no brightness changes into the microwave background radiation: uniform surface brightness backgrounds are unaffected by lensing (the Eikonal equation is sometimes cited). This is not true: gravitational lensing can introduce brightness fluctuations in a uniform background if the lens is non-static, for example if the lens is moving. This leads to an interesting test for the motion of large masses in the distant Universe (which I got wrong in my first paper on the subject in 1994, but got right in the paper below).

Birkinshaw, M., 1989. In Gravitational Lenses, eds. Moran, J., Hewitt, J. & Lo, K.Y.; Springer-Verlag, Berlin: Moving gravitational lenses

Sachs-Wolfe effect

This process, which introduces an important class of perturbations into the brightness of the microwave background radiation, may be regarded in a number of ways: but see below for the most physically meaningful (in my mind).

Perturbed spacetimes

It can be shown that the above two effects (and several other effects) are special cases of a single physical process, the effect of metric perturbations on the propagation of light. This topic has been addressed by

Pyne, T. & Birkinshaw, M., ApJ, 415, 459 (1993): Null geodesics in perturbed spacetimes
Pyne, T. & Birkinshaw, M., ApJ, 458, 46 (1996): Beyond the thin lens approximation
Pyne, T. et al., ApJ, 465, 566 (1996): Gravitational radiation and very long basline interferometry

Revised 27-Sep-1996 by Mark Birkinshaw