We show that a spherically symmetric perturbation of a dust dominated Ω = 1 FRW universe in the Newtonian gauge can lead to an apparent acceleration of standard candles and provide a fit to the magnitude-redshift relation inferred from the supernovae data, while the perturbation in the gravitational potential remains small at all scales. We also demonstrate that the supernovae data does not necessarily imply the presence of some additional non-perturbative contribution by showing that any Lemaitre-Tolman-Bondi model fitting the supernovae data (with appropriate initial conditions) will be equivalent to a perturbed FRW spacetime along the past light cone.

Using the spherically symmetric inhomogeneous Lemaître-Tolman-Bondi dust solution, we study how the shear and the backreaction depend on the sharpness of the spatial transition between voids and walls and on the size of the voids. The voids considered here are regions with matter density Ω 0 ≃ 0 and expansion rate H 0 t 0 ≃ 1, while the walls are regions with matter density Ω 0 ≃ 1 and expansion rate H 0 t 0 ≃ 2/3. The results indicate that both the volume-average shear and the variance of the expansion rate grow proportional to the sharpness of the transition and diverge in the limit of a step function, but, for realistic-sized voids, are virtually independent of the size of the void. However, the backreaction, given by the difference of the variance and the shear, has a finite value in the step-function limit. By comparing the exact result for the backreaction to the case where the shear is neglected by treating the voids and walls as separate Friedmann-Robertson-Walker models, we find that the shear suppresses the backreaction by a factor of (r 0 /t 0 ) 2 , the squared ratio of the void size to the horizon size. This exemplifies the importance of using the exact solution for the interface between the regions of different expansion rates and densities. The suppression is justified to hold also for a network of compensated voids, but may not hold if the universe is dominated by uncompensated voids.

Abstract:We study the effect of shear on the cosmological backreaction in the context of matching voids and walls together using the exact inhomogeneous Lemaître-Tolman-Bondi solution. Generalizing JCAP 1010 (2010) 021, we allow the size of the voids to be arbitrary and the densities of the voids and walls to vary in the range 0 ≤ Ω v ≤ Ω w ≤ 1. We derive the exact analytic result for the backreaction and consider its series expansion in powers of the ratio of the void size to the horizon size, r 0 /t 0 . In addition, we deduce a very simple fitting formula for the backreaction with error less than 1% for voids up to sizes r 0 t 0 . We also construct an exact solution for a network of voids with different sizes and densities, leading to a non-zero relative variance of the expansion rate between the voids. While the leading order term of the backreaction for a single void-wall pair is of order (r 0 /t 0 ) 2 , the relative variance between the different voids in the network is found to be of order (r 0 /t 0 ) 4 and thus very small for voids of the observed size. Furthermore, we show that even for very large voids, the backreaction is suppressed by an order of magnitude relative to the estimate obtained by treating the walls and voids as disjoint Friedmann solutions. Whether the suppression of the backreaction due to the shear is just a consequence of the restrictions of the used exact models, or a generic feature, has to be addressed with more sophisticated solutions.