Cosmological observables in a swiss-cheese universe

Photon geodesics are calculated in a Swiss-cheese model, where the cheese is made of the usual Friedmann-Robertson-Walker (FRW) solution and the holes are constructed from a Lemaître-Tolman-Bondi solution of Einstein’s equations. The observables on which we focus are the changes in the redshift, in the angular-diameter-distance relation, in the luminosity-distance-redshift relation, and in the corresponding distance modulus. We find that redshift effects are suppressed when the hole is small because of a compensation effect acting on the scale of half a hole resulting from the special case of spherical symmetry. However, we find interesting effects in the calculation of the angular distance: strong evolution of the inhomogeneities (as in the approach to caustic formation) causes the photon path to deviate from that of the FRW case. Therefore, the inhomogeneities are able to partly mimic the effects of a dark-energy component. Our results also suggest that the nonlinear effects of caustic formation in cold dark matter models may lead to interesting effects on photon trajectories.