Late-time Inhomogeneity and Acceleration Without Dark Energy

Abstract

The inhomogeneous distribution of matter in the non-linear regime of galaxies, clusters of galaxies and voids is described by an exact, spherically symmetric inhomogeneous solution of Einstein's gravitational field equations, corresponding to an under-dense void. The solution becomes the homogeneous and isotropic Einstein-de Sitter solution for a red shift $z > 10-20$, which describes the matter dominated CMB data with small inhomogeneities $δρ/ρ\sim 10^{-5}$. A spatial volume averaging of physical quantities is introduced and the averaged time evolution expansion parameter $θ$ in the Raychoudhuri equation can give rise in the late-time universe to a volume averaged deceleration parameter $<q>$ that is negative for a positive matter density. This allows for a region of accelerated expansion which does not require a negative pressure dark energy or a cosmological constant. A negative deceleration parameter can be derived by this volume averaging procedure from the Lemaître-Tolman-Bondi open void solution, which describes the late-time non-linear regime associated with galaxies and under-dense voids and solves the ``coincidence'' problem.

LaTex file, 16 pages, no figures. Typo corrections. References added and updated. Additional material and some conclusions changed. Replacement to match final published version in Journ. Cosmol. Astropart. Phys. JCAP 2006