Luminosity distance in Swiss cheese cosmology with randomized voids and galaxy halos

Abstract

We study the fluctuations in luminosity distance due to gravitational lensing produced both by galaxy halos and large scale voids. Voids are represented via a "Swiss cheese" model consisting of a \LambdaCDM Friedman-Robertson-Walker background in which a number of randomly distributed, spherical regions of comoving radius 35 Mpc are removed. A fraction of the removed mass is then placed on the shells of the spheres, in the form of randomly located halos, modeled with Navarro-Frenk-White profiles. The remaining mass is placed in the interior of the spheres, either smoothly distributed, or as randomly located halos. We compute the distribution of magnitude shifts using a variant of the method of Holz & Wald (1998), which includes the effect of lensing shear. In the two models we consider, the standard deviation of this distribution is 0.065 and 0.072 magnitudes and the mean is -0.0010 and -0.0013 magnitudes, for voids of radius 35 Mpc, sources at redshift 1.5, with the voids chosen so that 90% of the mass is on the shell today. The standard deviation due to voids and halos is a factor ~ 3 larger than that due to 35 Mpc voids alone with a 1 Mpc shell thickness which we studied in our previous work. To a good approximation, the variance of the distribution depends only on the mean column depth and concentration of halos and on the fraction of the mass density that is in the form of halos (as opposed to smoothly distributed): it is independent of how the halos are distributed in space. We derive an approximate analytic formula for the variance that agrees with our numerical results to \lesssim 20% out to z\simeq 1.5.

16 pages, 13 figures

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