On the bias of the distanceredshift relation from gravitational lensing
Abstract
A longstanding question in cosmology is whether gravitational lensing changes the distanceredshift relation D (z) or the mean flux density of sources. Interest in this has been rekindled by recent studies in nonlinear relativistic perturbation theory that find biases in both the area of a surface of constant redshift and in the mean distance to this surface, with a fractional bias in both cases of the order of the mean squared convergence <κ^{2}>. Any such area bias could alter cosmic microwave background (CMB) cosmology, and the corresponding bias in mean flux density could affect supernova cosmology. We show that the perturbation to the area of a surface of constant redshift is in reality much smaller, being of the order of the cumulative bending angle squared, or roughly a partinamillion effect. This validates the arguments of Weinberg that the mean magnification of sources is unity and of Kibble & Lieu that the mean directionaveraged inverse magnification is unity. It also validates the conventional treatment of CMB lensing. But the existence of a scatter in magnification will cause any nonlinear function of these conserved quantities to be statistically biased. The fractional bias in such quantities is generally of order <κ^{2}>, which is orders of magnitude larger than the area perturbation. Claims for large bias in area or flux density of sources appear to have resulted from misinterpretation of such effects: they do not represent a new nonNewtonian effect, nor do they invalidate standard cosmological analyses.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 February 2016
 DOI:
 10.1093/mnras/stv2585
 arXiv:
 arXiv:1503.08506
 Bibcode:
 2016MNRAS.455.4518K
 Keywords:

 cosmic background radiation;
 cosmology: observations;
 cosmology: theory;
 distance scale;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 32 pages, 5 figures, submitted to MNRAS