# Impact of modelling foreground uncertainties on future CMB polarization satellite experiments

## TL;DR

This study assesses how residual foreground modeling errors impact the measurement of the tensor-to-scalar ratio in future CMB polarization satellite experiments, highlighting the importance of precise foreground characterization.

## Contribution

It introduces a comprehensive pipeline for analyzing foreground residuals' effects on $r$ measurement, demonstrating the conditions for successful detection at different $r$ levels.

## Key findings

- Successful measurement of r=0.01 despite complex foregrounds.
- Bias in r measurement increases with inaccurate foreground spectral modeling.
- Precise foreground spectral index knowledge (≤0.5\\%) is crucial for detecting r=0.001.

## Abstract

We present an analysis of errors on the tensor-to-scalar ratio due to residual diffuse foregrounds. We use simulated observations of a CMB polarization satellite, the Cosmic Origins Explorer, using the specifications of the version proposed to ESA in 2010 (COrE). We construct a full pipeline from microwave sky maps to $r$ likelihood, using two models of diffuse Galactic foregrounds with different complexity, and assuming component separation with varying degrees of accuracy. Our pipeline uses a linear mixture (Generalized Least Squares) solution for component separation, and a hybrid approach for power spectrum estimation, with a Quadratic Maximum Likelihood estimator at low $\ell$s and a pseudo-$C_{\ell}$ deconvolution at high $\ell$s. In the likelihood for $r$, we explore modelling foreground residuals as nuisance parameters. Our analysis aims at measuring the bias introduced in $r$ by mismodelling the foregrounds, and to determine what error is tolerable while still successfully detecting $r$. We find that $r=0.01$ can be measured successfully even for a complex sky model and in the presence of foreground parameters error. However, the detection of $r=0.001$ is a lot more challenging, as inaccurate modelling of the foreground spectral properties may result in a biased measurement of $r$. Once biases are eliminated, the total error on $r$ allows setting an upper limit rather than a detection, unless the uncertainties on the foreground spectral indices are very small, i.e. equal or better than 0.5\% error for both dust and synchrotron. This emphasizes the need for pursuing research on component separation and foreground characterization in view of next-generation CMB polarization experiments.