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Abstract: Using the spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi dustsolution, we study how the shear and the backreaction depend on the sharpnessof 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 andexpansion rate Ht ~ 1, while the walls are regions with matter density Omega ~1 and expansion rate Ht ~ 2-3. The results indicate that both thevolume-average shear and the variance of the expansion rate grow proportionalto 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 thevoid. However, the backreaction, given by the difference of the variance andthe shear, has a finite value in the step-function limit. By comparing theexact result for the backreaction to the case where the shear is neglected bytreating the voids and walls as separate Friedmann-Robertson-Walker models, wefind that the shear suppresses the backreaction by a factor of r 0-t 0^2, thesquared ratio of the void size to the horizon size. This exemplifies theimportance of using the exact solution for the interface between the regions ofdifferent expansion rates and densities. The suppression is justified to holdalso for a network of compensated voids, but may not hold if the universe isdominated by uncompensated voids.

Autor: Maria Mattsson, Teppo Mattsson

Fuente: https://arxiv.org/


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