Gravitational lensing in observational cosmology

Abstract

This paper reviews some previous theoretical and observational results concerning the various effects of gravitational lensing, and also presents still unpublished results in this field. The theoretical section deals with the Optical Scalar Equation (OSE) approach. We recall the form of these equations, which relate the deformations of the cross sectional area of a light beam to the material and energetic distribution it encounters, via the two basic contributions to lensing, the matter or Ricci term and the shear term. The introduction of a new distance, the optical distance, allows to write the OSE in a simplified way from which new solutions are easily derived. We demonstrate here that a general form may be obtained for the amplification formula in the exact relativistic treatment, provided the Universe is assumed to be Friedmannian in the mean. New results are also presented concerning the probability distribution of amplifications, the relation from matter term to shear terms (the first ones give the mean of the second ones) and the problem of energy conservation. We recall how our method let to an analytical formula yielding the amplification by any number of lenses placed anywhere along the line of sight and present new general solutions for lensing by large scale density inhomogeneities. The gravitational redshift effects are also considered, either due to the crossing by photons of inhomogeneities, or intrinsic to them ; generalized solutions to the last problem are given. Some observational evidence concerning various lensing effects, either statistical or applying to individual sources, are considered. We first recall how the dependence of the amplification formula on the various physical parameters points towards the optimisation of lensing by very rich clusters of galaxies lying at redshifts around 0.7, which may give rise to very large amplifications for reasonable values of the density parameter. Recent results concerning a statistical effect of amplification of Brightest Cluster Galaxies by foreground clusters are analysed, including the discussion of a selection effect precisely due to gravitational luminosity amplification. It results in an artificial increase of the deceleration parameter of the Universe measured from the Hubble diagram of these objects. We recall our proposal that the sample of distant 3C radiogalaxies of redshift > 1 is strongly perturbed by lensing effects, mostly by foreground clusters of galaxies (i.e. only the luminosity is changed without image multiplication), but also for some objects by galaxies, producing gravitational mirages. The case of 3C324, for which definite evidence for multiple imaging has been recently obtained, is described, including detailed modelling of the lensing configuration. We present a highly significant statistical effect of lensing on absorption line QSOs due to matter lying at the absorption redshifts. Microlensing is also considered, and we recall our recent proposal that the variability of some among the OVV QSOs turning to BL Lac at maximum brightness, like the eruptive object 0846 +51W1, is a consequence of microlensing by stars or compact objects constituting foreground galaxy halos. Finally, discrepant redshift associations are considered. We recall how the case of anomalous quintets of galaxies have been explained by the gravitational lensing effects of quartets halos on background galaxies. Then we present evidence that the Arp QSO-galaxy associations may be the result of the combined lensing effects of several superposed galaxies, groups and clusters.