Lensing and caustic effects on cosmological distances

We consider the changes which occur in cosmological distances due to the combined effects of some null geodesics passing through low-density regions while others pass through lensing-induced caustics. This combination of effects increases observed areas corresponding to a given solid angle even when averaged over large angular scales, through the additive effect of increases on all scales, but particularly on micro-angular scales; however angular sizes will not be significantly effected on large angular scales (when caustics occur, area distances and angular-diameter distances no longer coincide). We compare our results with other works on lensing, which claim there is no such effect, and explain why the effect will indeed occur in the (realistic) situation where caustics due to lensing are significant. Whether or not the effect is significant for number counts depends on the associated angular scales and on the distribution of inhomogeneities in the universe. It could also possibly affect the spectrum of CBR anisotropies on small angular scales, indeed caustics can induce a non-Gaussian signature into the CMB at small scales and lead to stronger mixing of anisotropies than occurs in weak lensing.Comment: 28 pages, 6 ps figures, eps

Light Propagation and Large-Scale Inhomogeneities

We consider the effect on the propagation of light of inhomogeneities with sizes of order 10 Mpc or larger. The Universe is approximated through a variation of the Swiss-cheese model. The spherical inhomogeneities are void-like, with central underdensities surrounded by compensating overdense shells. We study the propagation of light in this background, assuming that the source and the observer occupy random positions, so that each beam travels through several inhomogeneities at random angles. The distribution of luminosity distances for sources with the same redshift is asymmetric, with a peak at a value larger than the average one. The width of the distribution and the location of the maximum increase with increasing redshift and length scale of the inhomogeneities. We compute the induced dispersion and bias on cosmological parameters derived from the supernova data. They are too small to explain the perceived acceleration without dark energy, even when the length scale of the inhomogeneities is comparable to the horizon distance. Moreover, the dispersion and bias induced by gravitational lensing at the scales of galaxies or clusters of galaxies are larger by at least an order of magnitude.Comment: 27 pages, 9 figures, revised version to appear in JCAP, analytical estimate included, typos correcte