Sachs-Wolfe effect in some anisotropic models

Abstract

In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an `isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.