On the role of shear in cosmological averaging

TL;DR

This paper investigates how shear influences cosmological averaging in inhomogeneous models, showing that shear significantly suppresses backreaction effects, especially in realistic void configurations, emphasizing the importance of exact solutions at interfaces.

Contribution

It provides a detailed analysis of shear's role in backreaction within the Lemaître-Tolman-Bondi model, highlighting the suppression effect and the importance of exact interface solutions.

Findings

Shear and expansion variance grow with transition sharpness.

Backreaction remains finite in the step-function limit.

Shear suppresses backreaction by a factor proportional to the square of the void-to-horizon size ratio.

Abstract

Using the spherically symmetric inhomogeneous Lemaitre-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 Omega ~ 0 and expansion rate Ht ~ 1, while the walls are regions with matter density Omega ~ 1 and expansion rate Ht ~ 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.