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

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.Comment: 28 pages, 26 Fig

CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions

CMB anisotropy measurements have brought the issue of global topology of the universe from the realm of theoretical possibility to within the grasp of observations. The global topology of the universe modifies the correlation properties of cosmic fields. In particular, strong correlations are predicted in CMB anisotropy patterns on the largest observable scales if the size of the Universe is comparable to the distance to the CMB last scattering surface. We describe in detail our completely general scheme using a regularized method of images for calculating such correlation functions in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic spaces. Our procedure directly sums over images within a specified radius, ideally many times the diameter of the space, effectively treats more distant images in a continuous approximation, and uses Cesaro resummation to further sharpen the results. At all levels of approximation the symmetries of the space are preserved in the correlation function. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. Although the eigenspectrum can be obtained by this method if desired, at a given level of approximation the correlation functions are more accurately determined. We use the 3-torus example to demonstrate that the method works very well. We apply it to power spectrum as well as correlation function evaluations in a number of compact hyperbolic (CH) spaces. Application to the computation of CMB anisotropy correlations on CH spaces, and the observational constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11, 199