The Effect of Gravitational Lensing on Cosmological Parameter Estimation
A very long standing question in cosmology is whether gravitational lensing biases the distance-redshift relation D(z) or the mean flux density of sources. Interest in this has been rekindled by recent results in 2nd order relativistic perturbation theory which, if correct, would have profound implications for cosmological parameter estimation from both SN1a and the CMB. In this talk I shall first review the somewhat confusing history of the subject, going back to the early '60s and including both Weinberg's 1976 argument that there should be no effect on grounds of flux conservation and the general relativistic "focusing theorem" of the '80s that foreshadows the more recent results. I then show how the claimed subtle relativistic effects actually result from confusion between different types of averaging (specifically between averaging over sources and averaging over directions on the sky). I also show that while Weinberg's argument conceals a hidden loop-hole, in that he assumes that the area of a surface of constant redshifts is unaffected by lensing, the error incurred is only a one part in a million effect. This result validates conventional methods for analysis of the CMB and shows that, counter to claims in the literature, the focusing theorem does not in fact reveal an intrinsic tendency for structure to cause focusing of light rays.