On the bias of the distance-redshift relation from gravitational lensing

Nick Kaiser, John A. Peacock

Research output: Contribution to journalArticlepeer-review

Abstract

A long-standing question in cosmology is whether gravitational lensing changes the distance-redshift relation D (z) or the mean flux density ofsources. Interest in this has been rekindled by recent studies innon-linear relativistic perturbation theory that find biases in both thearea of a surface of constant redshift and in the mean distance to thissurface, with a fractional bias in both cases of the order of the meansquared convergence . Any such area biascould alter cosmic microwave background (CMB) cosmology, and thecorresponding bias in mean flux density could affect supernovacosmology. We show that the perturbation to the area of a surface ofconstant redshift is in reality much smaller, being of the order of thecumulative bending angle squared, or roughly a part-in-a-million effect. This validates the arguments of Weinberg that the mean magnification ofsources is unity and of Kibble & Lieu that the meandirection-averaged inverse magnification is unity. It also validates theconventional treatment of CMB lensing. But the existence of a scatter inmagnification will cause any non-linear function of these conservedquantities to be statistically biased. The fractional bias in suchquantities is generally of order , which isorders of magnitude larger than the area perturbation. Claims for largebias in area or flux density of sources appear to have resulted frommisinterpretation of such effects: they do not represent a newnon-Newtonian effect, nor do they invalidate standard cosmological analyses.
Original languageEnglish
Pages (from-to)4518-4547
Number of pages30
JournalMonthly Notices of the Royal Astronomical Society
Volume455
Issue number4
Early online date10 Dec 2015
DOIs
Publication statusPublished - 1 Feb 2016

Keywords

  • cosmic background radiation
  • cosmology: observations
  • cosmology: theory
  • distance scale

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