SEMI-BLIND EIGEN ANALYSES OF RECOMBINATION HISTORIES USING COSMIC MICROWAVE BACKGROUND DATA

Abstract

Cosmological parameter measurements from cosmic microwave background (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 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 freezeout 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 from the fiducial recombination model computed with Recfast, Xe, i(z), toward the precise underlying history given by the new and improved recombination calculations of CosmoRec or HyRec, Xe, 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 Xe, 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) freezeout tail, as would be appropriate when looking for the Xe signature of annihilating or decaying elementary particles.