On the role of shear in cosmological averaging II: large voids, non-empty voids and a network of different voids

Abstract

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.

Inhomogeneous cosmology and backreaction: Current status and future prospects

“…This was shown for the LT model. 44,45 For the Szekeres model with the central observer, the averaging wipes out the dipole and the result of averaging leads to the same conclusions as for the Lemaître-Tolman model. 46 In order to obtain large backreaction or large observational effects for these types of models one needs to consider ultra large scales, i.e., of order (or even larger) of Gpc scales.…”

Observational aspects of an inhomogeneous cosmology

“…Recently there have been several papers [21,22,23,24,25,26,27,18,10] , which show that the magnitude and importance of these backreactions is still a topic of hot discussion. Timescape cosmology and similar inhomogeneous cosmologies may provide possible solutions for the dark energy problem, but the estimates of the magnitude of backreaction from voids and their influence on the expansion of the universe range from negligible to extremely important [28,29,26,14]. Therefore, observational tests are essential for the ongoing debate.…”

Averaging in LRS class II spacetimes

“…First, we investigate the backreaction term in Buchert's equation (25). We numerically integrate the underlined part of equation (25) depending on the averaging scale l. As one can see from Figure 2, the backreaction normalized by θ · is negative.…”

“…By averaging we can not leave this class, instead we may end up in a special subclass of LRS class II dust models. We performed averaging of the evolution equation for expansion (25) and of the evolution equations for different products of expansion, shear, density and electric part of the Weyl tensor. From this construction we can see that the averaged equations contain an averaged LTB model, but generally not e.g.…”