Structured FRW universe leads to acceleration: a non-perturbative approach

Abstract

We propose a model universe in the matter dominated phase described by a FRW background with local inhomogeneities, like our local patch, grown out of the primordial fluctuations. Our sub-horizon local patch consisting of different structures is approximated as an inhomogeneous cosmic fluid described by a LTB metric embedded in a background FRW universe, in which the observer could be located anywhere. Within the exact general relativistic formulation, the junction conditions for the only possible matching without a thin shell at the boundary, neglected so far in the literature, constrains the model in such a way that the luminosity distance-red shift relation mimics a FRW universe with dark energy. Therefore, the dimming of SNIa is accounted for in such a {\it structured} FRW universe. We have also calculated the exact general relativistic backreaction term and shown how it influences the global Hubble parameter and the effective density of the cosmic fluid By using an exact formulation of the general relativistic dynamics of structures in a homogeneous universe, the claim is therefore stressed that the backreaction of cosmological perturbations leads to an apparent dimming of the cosmological distances.