Extreme data compression for the CMB

Abstract

We apply the Karhunen-Loéve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in $\Lambda$ cold dark matter cosmologies in under a minute, much faster than Markov chain Monte Carlo methods. This is achieved by forming a linear combination of the power spectra at each multipole $l$, and solving a system of simultaneous equations such that the Fisher matrix is locally unchanged. Instead of carrying out a full likelihood evaluation over the whole parameter space, we need evaluate the likelihood only for the parameter of interest, with the data compression effectively marginalizing over all other parameters. The weighting vectors contain insight about the physical effects of the parameters on the CMB anisotropy power spectrum $C_l$. The shape and amplitude of these vectors give an intuitive feel for the physics of the CMB, the sensitivity of the observed spectrum to cosmological parameters, and the relative sensitivity of different experiments to cosmological parameters. We test this method on exact theory $C_l$ as well as on a Wilkinson Microwave Anisotropy Probe (WMAP)-like CMB data set generated from a random realization of a fiducial cosmology, comparing the compression results to those from a full likelihood analysis using CosmoMC. After showing that the method works, we apply it to the temperature power spectrum from the WMAP seven-year data release, and discuss the successes and limitations of our method as applied to a real data set.

14 pages, 14 figures, 2 tables, updated to match the published version in PRD

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• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
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• Data compression in cosmology: A compressed likelihood for Planck data
• Non-linear shrinkage estimation of large-scale structure covariance
• KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear
• candl: Cosmic Microwave Background Analysis with a Differentiable Likelihood
• Data Compression and Inference in Cosmology with Self-Supervised Machine Learning
• Extreme data compression while searching for new physics
• Joint constraints on reionization: a framework for combining the global 21cm signal and the kinetic Sunyaev-Zel'dovich effect
• Data Compression and Covariance Matrix Inspection: Cosmic Shear
• Skew-spectra: a generalization to spin-$s$