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

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, X-e(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 X-e(z) with CMB measurements. Since the eigenmodes are effectively weighed by the fiducial X-e 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, X-e,X-i(z), toward the precise underlying history given by the new and improved recombination calculations of COSMOREC or HYREC, X-e,X-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-e,X-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 X-e(z) freezeout tail, as would be appropriate when looking for the X-e signature of annihilating or decaying elementary particles.