Compressed 'CMB-lite' Likelihoods Using Automatic Differentiation

TL;DR

This paper introduces a fast, accurate method for creating compressed CMB likelihoods using automatic differentiation, significantly reducing computational costs while maintaining high fidelity in cosmological parameter estimation.

Contribution

It presents a novel implementation of the CMB-lite framework that relies on automatic differentiation, enabling rapid likelihood construction on personal computers.

Findings

Likelihood construction time reduced to about a minute.

Good agreement with multi-frequency likelihoods in parameter posteriors.

Parameter estimates shift by less than 0.1 sigma, with errors within 10%.

Abstract

The compression of multi-frequency cosmic microwave background (CMB) power spectrum measurements into a series of foreground-marginalised CMB-only band powers allows for the construction of faster and more easily interpretable 'lite' likelihoods. However, obtaining the compressed data vector is computationally expensive and yields a covariance matrix with sampling noise. In this work, we present an implementation of the CMB-lite framework relying on automatic differentiation. The technique presented reduces the computational cost of the lite likelihood construction to one minimisation and one Hessian evaluation, which run on a personal computer in about a minute. We demonstrate the efficiency and accuracy of this procedure by applying it to the differentiable SPT-3G 2018 TT/TE/EE likelihood from the candl library. We find good agreement between the marginalised posteriors of cosmological parameters yielded by the resulting lite likelihood and the reference multi-frequency version for all cosmological models tested; the best-fit values shift by $<0.1\,\sigma$, where $\sigma$ is the width of the multi-frequency posterior, and the inferred parameter error bars match to within $<10\%$. We publicly release the SPT-3G 2018 TT/TE/EE lite likelihood and a python notebook showing its construction at https://github.com/Lbalkenhol/candl .