Does Gravitational Lensing Affect The Cosmological Distance-Redshift Relation?

A long standing question in cosmology is whether gravitational lensing changes the mean distance-redshift relation or the mean flux density of sources.

I will first review the rich history of this subject. The problem was first considered by Zel'dovich in the early '60s and reconsidered by many other since. Yet the situation remains confused. Weinberg, for example, argued in '76 that there is no effect on the grounds of flux conservation, yet that seems to conflict with other calculations. Interest in this has been rekindled by recent results from 2nd order relativistic perturbation theory which, if correct, would have profound implications for both supernova and CMB cosmology.

With John Peacock, I revisit this. First, we argue, drawing on Kibble and Lieu, that many of the apparent contradictions can be understood as arising from confusion between different types of averaging. Second, we carefully examine Weinberg's argument that there should be no effect and show that the fractional perturbation to the area of a surface of constant source redshift is one part in a million effect. This effectively validates the conventional approach to CMB analysis and provides a firm basis for SN1a cosmology.