Cosmic microwave background, accelerating universe and inhomogeneous cosmology

We consider a cosmology in which a spherically symmetric large scale inhomogeneous enhancement or a void are described by an inhomogeneous metric and Einstein's gravitational equations. For a. at matter dominated universe the inhomogeneous equations lead to luminosity distance and Hubble constant formulae that depend on the location of the observer. For a general inhomogeneous solution, it is possible for the deceleration parameter to differ. er signifi. cantly from the FLRW result. The deceleration parameter q0 can be interpreted as q0 > 0 in a FLRW universe (q0 = 1/2 for a flat matter dominated universe) and q0 < 0 as inferred from the inhomogeneous enhancement that is embedded in a FLRW universe. A spatial volume averaging of local regions in the backward light cone has to be performed for the inhomogeneous solution at late times to decide whether the decelerating parameter q0 can be negative for a positive energy condition. The CMB temperature. fluctuations across the sky can be unevenly distributed in the northern and southern hemispheres in the inhomogeneous matter dominated solution, in agreement with the analysis of the WMAP power spectrum data by several authors. The model can possibly explain the anomalous alignment of the quadrupole and octopole moments observed in the WMAP data.