CMB sky for an off-center observer in a local void I: framework for
  forecasts
  The Universe is not perfectly homogeneous, the large scale structure forms
overdense 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
underdense 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 addition to the non-stochastic CMB
anisotropies due to the geometry of the model, we also observe a lensing-like
distortion of the CMB anisotropies. In this article, we propose a framework to
forecast the precision with which we can measure the amplitude of the
lensing-like deformation of the CMB temperature anisotropies. For illustrative
purposes, 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.
