PROFESSOR NICHOLAS KAISER

A long standing question in cosmology is whether gravitational lensing changes the mean distance-redshift relation D(z) or the mean flux density of sources. In this talk I will first review the rich history of this subject. The problem was first considered by Jacob Zel'dovich in the early '60s and reconsidered by many other since. Yet the situation remains confused. Steven 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, this would have profound implications for both supernova and CMB cosmology. John Peacock and I have recently revisited this. In our paper we make two main points: First, we argue, drawing on Kibble and Lieu, that many of the apparent contradictions and recently claimed large effects can be understood as arising from confusion between different types of averaging (specifically between averaging over sources and averaging over directions on the sky). Second, we carefully examine Weinberg's argument that there should be no effect. In this he makes the implicit assumption that the area of a surface of constant source redshift is unperturbed by lensing. We have shown by direct calculation that, while this is not strictly correct, the fractional perturbation to the area is an effect that is on the order of the cumulative light defelection angle squared, or about a one part in a million effect. This effectively validates the conventional approach to CMB analysis and provides a firm basis for SN1a cosmology.