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

## TL;DR

This paper develops a framework to forecast how well future CMB observations can detect lensing-like distortions caused by our potential off-center position in a local cosmic void, highlighting the detectability with Planck data.

## Contribution

It introduces a novel method to predict the measurement precision of lensing-like CMB anisotropy distortions in inhomogeneous universe models with local voids.

## Key findings

- Planck data could potentially detect lensing-like effects in large void models.
- The framework allows forecasting measurement accuracy for off-center observer effects.
- Application to specific void models demonstrates the method's practical utility.

## Abstract

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.