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We study the fluctuations in luminosity distance due to gravitational lensingproduced both by galaxy halos and large scale voids. Voids are represented viaa "Swiss cheese" model consisting of a \LambdaCDM Friedman-Robertson-Walkerbackground in which a number of randomly distributed, spherical regions ofcomoving radius 35 Mpc are removed. A fraction of the removed mass is thenplaced 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 theinterior of the spheres, either smoothly distributed, or as randomly locatedhalos. We compute the distribution of magnitude shifts using a variant of themethod of Holz & Wald (1998), which includes the effect of lensing shear. Inthe two models we consider, the standard deviation of this distribution is0.065 and 0.072 magnitudes and the mean is -0.0010 and -0.0013 magnitudes, forvoids of radius 35 Mpc, sources at redshift 1.5, with the voids chosen so that90% of the mass is on the shell today. The standard deviation due to voids andhalos is a factor ~ 3 larger than that due to 35 Mpc voids alone with a 1 Mpcshell thickness which we studied in our previous work. To a good approximation,the variance of the distribution depends only on the mean column depth andconcentration of halos and on the fraction of the mass density that is in theform of halos (as opposed to smoothly distributed): it is independent of howthe halos are distributed in space. We derive an approximate analytic formulafor the variance that agrees with our numerical results to \lesssim 20% out toz\simeq 1.5.

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