Semi-blind Eigen-analyses of Recombination Histories Using CMB Data

TL;DR

This paper develops a semi-blind eigenmode approach to analyze perturbations in the recombination history from CMB data, enabling more accurate cosmological parameter estimation and potential detection of new physics.

Contribution

It introduces a new eigenmode-based method to probe deviations in the free electron fraction during recombination, improving the analysis of CMB data and bias mitigation.

Findings

Eigenmodes effectively probe hydrogen recombination history.

Few modes can significantly improve recombination models.

Method can be tailored to focus on specific redshift regimes.

Abstract

Cosmological parameter measurements from CMB experiments such as Planck, ACTpol, SPTpol and other high resolution follow-ons fundamentally rely on the accuracy of the assumed recombination model, or one with well prescribed uncertainties. Deviations from the standard recombination history might suggest new particle physics or modified atomic physics. Here we treat possible perturbative fluctuations in the free electron fraction, $\Xe(z)$, by a semi-blind expansion in densely-packed modes in redshift. From these we construct parameter eigenmodes, which we rank order so that the lowest modes provide the most power to probe the $\Xe(z)$ with CMB measurements. Since the eigenmodes are effectively weighed by the fiducial $\Xe$ history, they are localized around the differential visibility peak, allowing for an excellent probe of hydrogen recombination, but a weaker probe of the higher redshift helium recombination and the lower redshift highly neutral freeze-out tail. We use an information-based criterion to truncate the mode hierarchy, and show that with even a few modes the method goes a long way towards morphing a fiducial older {\sc Recfast} $X_{\rm e,i} (z)$ into the new and improved {\sc CosmoRec} and {\sc HyRec} $X_{\rm e,f} (z)$ in the hydrogen recombination regime, though not well in the helium regime. Without such a correction, the derived cosmic parameters are biased. We discuss an iterative approach for updating the eigenmodes to further hone in on $X_{\rm e,f} (z)$ if large deviations are indeed found. We also introduce control parameters that downweight the attention on the visibility peak structure, e.g., focusing the eigenmode probes more strongly on the $\Xe (z)$ freeze-out tail, as would be appropriate when looking for the $\Xe$ signature of annihilating or decaying elementary particles.