Abstract. We construct the first exact statistically homogeneous and isotropic cosmological solution in which inhomogeneity has a significant effect on the expansion rate. The universe is modelled as a Swiss Cheese, with dust FRW background and inhomogeneous holes. We show that if the holes are described by the quasispherical Szekeres solution, their average expansion rate is close to the background under certain rather general conditions. We specialise to spherically symmetric holes and violate one of these conditions. As a result, the average expansion rate at late times grows relative to the background, i.e. backreaction is significant. The holes fit smoothly into the background, but are larger on the inside than a corresponding background domain: we call them Tardis regions. We study light propagation, find the effective equations of state and consider the relation of the spatially averaged expansion rate to the redshift and the angular diameter distance.

The discovery of a void of size ∼200h −1 Mpc and average density contrast of ∼ − 0.1 aligned with the cold spot direction has been recently reported. It has been argued that, although the first-order integrated Sachs-Wolfe (ISW) effect of such a void on the cosmic microwave background is small, the second-order Rees-Sciama (RS) contribution exceeds this by an order of magnitude and can entirely explain the observed cold spot temperature profile. In this paper we examine this surprising claim using both an exact calculation with the spherically symmetric Lemaître-Tolman-Bondi metric, and perturbation theory about a background Friedmann-Robertson-Walker metric. We show that both approaches agree well with each other, and both show that the dominant temperature contribution of the postulated void is an unobservable dipole anisotropy. If this dipole is subtracted, we find that the remaining temperature anisotropy is dominated by the linear ISW signal, which is orders of magnitude larger than the second-order RS effect, and that the total magnitude is too small to explain the observed cold spot profile. We calculate the density and size of a void that would be required to explain the cold spot, and show that the probability of existence of such a void is essentially zero in ΛCDM. We identify the importance of a posteriori selection effects in the identification of the cold spot, but argue that even after accounting for them, a supervoid explanation of the cold spot is always disfavored relative to a random statistical fluctuation on the last scattering surface.

Abstract. We consider a Swiss Cheese model with a random arrangement of Lemaître-Tolman-Bondi holes in ΛCDM cheese. We study two kinds of holes with radius r b = 50 h −1 Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB. We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra.In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95% limit |∆D A /D A | 10 −4 .We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. The closed case is consistent with this at 1σ, whereas in the open case the probability is only 1.4%.