The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra

TL;DR

This paper develops and validates an analytic covariance matrix method for the ACT DR6 CMB power spectrum, achieving high accuracy and improving error modeling for cosmological analysis, with potential application to future experiments.

Contribution

The paper introduces a semi-analytic covariance matrix prescription that accurately models ACT DR6 data, incorporating complex survey features and providing a correction method based on simulations.

Findings

Achieves better than 3% agreement with Monte Carlo simulations.

Improves upon previous covariance estimates with a new correction method.

Framework applicable to future high-resolution CMB experiments.

Abstract

The Atacama Cosmology Telescope Data Release 6 (ACT DR6) power spectrum is expected to provide state-of-the-art cosmological constraints, with an associated need for precise error modeling. In this paper we design, and evaluate the performance of, an analytic covariance matrix prescription for the DR6 power spectrum that sufficiently accounts for the complicated ACT map properties. We use recent advances in the literature to handle sharp features in the signal and noise power spectra, and account for the effect of map-level anisotropies on the covariance matrix. In including inhomogeneous survey depth information, the resulting covariance matrix prescription is structurally similar to that used in the $\textit{Planck}$ Cosmic Microwave Background (CMB) analysis. We quantify the performance of our prescription using comparisons to Monte Carlo simulations, finding better than $3\%$ agreement. This represents an improvement from a simpler, pre-existing prescription, which differs from simulations by $\sim16\%$. We develop a new method to correct the analytic covariance matrix using simulations, after which both prescriptions achieve better than $1\%$ agreement. This correction method outperforms a commonly used alternative, where the analytic correlation matrix is assumed to be accurate when correcting the covariance. Beyond its use for ACT, this framework should be applicable for future high resolution CMB experiments including the Simons Observatory (SO).