Constraining Cosmological Parameters with Needlet Internal Linear Combination Maps II: Likelihood-Free Inference on NILC Power Spectra

TL;DR

This paper introduces a likelihood-free inference method using NILC maps for better cosmological parameter estimation from CMB data, especially in the presence of non-Gaussian foregrounds, achieving significantly reduced uncertainties.

Contribution

It develops a novel NILC-based likelihood-free inference approach that improves parameter constraints by leveraging non-Gaussian information in CMB maps.

Findings

NILC maps yield smaller parameter error bars than traditional MFPS.

Likelihood-free inference with NILC reduces the 2D confidence region by 60%.

Method is promising for primordial B-mode searches with complex foregrounds.

Abstract

Standard cosmic microwave background (CMB) analyses constrain cosmological and astrophysical parameters by fitting parametric models to multifrequency power spectra (MFPS). However, such methods do not optimally weight maps in power spectrum (PS) measurements for non-Gaussian CMB foregrounds. We propose needlet internal linear combination (NILC), operating on wavelets with compact support in pixel and harmonic space, as a weighting scheme to yield more optimal parameter constraints. In a companion paper, we derived an analytic formula for NILC map PS, which is physically insightful but computationally difficult to use in parameter inference pipelines. In this work, we analytically show that fitting parametric templates to MFPS and harmonic ILC PS yields identical parameter constraints when the number of sky components equals or exceeds the number of frequency channels. We numerically show that, for Gaussian random fields, the same holds for NILC PS. This suggests that NILC can reduce parameter error bars in the presence of non-Gaussian fields since it uses non-Gaussian information. As Gaussian likelihoods may be inaccurate, we use likelihood-free inference (LFI) with neural posterior estimation. We show that performing inference with auto- and cross-PS of NILC component maps as summary statistics yields smaller parameter error bars than inference with MFPS. For a model with CMB, an amplified thermal Sunyaev--Zel'dovich (tSZ) signal, and noise, we find a 60% reduction in the area of the 2D 68% confidence region for component amplitude parameters inferred from NILC PS, as compared to inference from MFPS. Primordial $B$-mode searches are a promising application for our new method, as the amplitude of the non-Gaussian dust foreground is known to be larger than a potential signal. Our code is available in https://github.com/kmsurrao/NILC-Inference-Pipeline.