CMB Power Spectrum Likelihood with ILC

TL;DR

This paper enhances the ILC method in harmonic space to incorporate CMB estimate errors, enabling more accurate parameter estimation by accounting for foreground effects and subtraction errors, validated through simulations.

Contribution

It introduces a new likelihood approach that includes ILC errors in harmonic space, improving foreground handling in CMB analysis.

Findings

Method reduces sensitivity to foreground model errors

Simulations validate the likelihood calculations

Improves parameter estimation accuracy

Abstract

We extend the ILC method in harmonic space to include the error in its CMB estimate. This allows parameter estimation routines to take into account the effect of the foregrounds as well as the errors in their subtraction in conjunction with the ILC method. Our method requires the use of a model of the foregrounds which we do not develop here. The reduction of the foreground level makes this method less sensitive to unaccounted for errors in the foreground model. Simulations are used to validate the calculations and approximations used in generating this likelihood function.