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

Here we treat possible perturbative fluctuations in the free electron fraction, X sub(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 sub(e)(z) with CMB measurements. 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 sub(e,i)(z), toward the precise underlying history given by the new and improved recombination calculations of COSMOREC or HYREC, X sub(e,f)(z), in the hydrogen recombination regime, though not well in the helium regime. 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 X sub(e) signature of annihilating or decaying elementary particles.