CMB sky for an off-center observer in a local void I: framework for forecasts

Abstract

The Universe is not perfectly homogeneous, the large scale structure forms over dense regions and voids. In this paper we consider the possibility that we occupy a special position in our Universe, close to the center of a local under dense region that we model as an LTB void embedded in a homogeneous and isotropic Universe. The CMB sky measured by an off-center observer in this void is not statistically isotropic. In this article we propose a framework to forecast the precision with which we can measure the amplitude of the anisotropic contribution of the CMB temperature correlation function. We apply this method to a couple of large-scale void models differing over the matter density profile and we show that the CMB temperature data from the Planck satellite is potentially capable to detect the effect for the large voids chosen here. A companion paper will be dedicated to a systematic exploration of different realistic void models.