On the role of shear in cosmological averaging

Understand

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.