Cosmic microwave background, accelerating universe and inhomogeneous cosmology

Abstract

We consider a cosmology in which a spherically symmetric large scale inhomogeneousenhancement or a void are described by an inhomogeneous metric and Einstein’sgravitational equations. For a flat matter dominated universe the inhomogeneous equationslead to luminosity distance and Hubble constant formulae that depend on the location ofthe observer. For a general inhomogeneous solution, it is possible for the decelerationparameter to differ significantly from the FLRW result. The deceleration parameterq0 can be interpreted asq0 > 0 in a FLRW universe(q0 = 1/2 for a flat matterdominated universe) and q0 < 0 as inferred from the inhomogeneous enhancement that is embedded in a FLRW universe. Aspatial volume averaging of local regions in the backward light cone has to be performed forthe inhomogeneous solution at late times to decide whether the decelerating parameterq can be negative for a positive energy condition. The CMB temperature fluctuations acrossthe sky can be unevenly distributed in the northern and southern hemispheres in theinhomogeneous matter dominated solution, in agreement with the analysis of the WMAPpower spectrum data by several authors. The model can possibly explain the anomalousalignment of the quadrupole and octopole moments observed in the WMAP data.