Rico: An Accurate Cosmological Recombination Code

We present Rico, a code designed to compute the ionization fraction of the Universe during the epoch of hydrogen and helium recombination with an unprecedented combination of speed and accuracy. This is accomplished by training the machine learning code Pico on the calculations of a multi-level cosmological recombination code which self-consistently includes several physical processes that were neglected previously. After training, Rico is used to fit the free electron fraction as a function of the cosmological parameters. While, for example at low redshifts (z<~900), much of the net change in the ionization fraction can be captured by lowering the hydrogen fudge factor in Recfast by about 3%, Rico provides a means of effectively using the accurate ionization history of the full recombination code in the standard cosmological parameter estimation framework without the need to add new or refined fudge factors or functions to a simple recombination model. Within the new approach presented here it is easy to update Rico whenever a more accurate full recombination code becomes available. Once trained, Rico computes the cosmological ionization history with negligible fitting error in ~10 milliseconds, a speed-up of at least 10^6 over the full recombination code that was used here. Also Rico is able to reproduce the ionization history of the full code to a level well below 0.1%, thereby ensuring that the theoretical power spectra of CMB fluctuations can be computed to sufficient accuracy and speed for analysis from upcoming CMB experiments like Planck. Furthermore it will enable cross-checking different recombination codes across cosmological parameter space, a comparison that will be very important in order to assure the accurate interpretation of future cosmic microwave background data.Comment: 14 pages, 11 figures, submitted to PR

Probing the last scattering surface through the recent and future CMB observations

We have constrained the extended (delayed and accelerated) models of hydrogen recombination, by investigating associated changes of the position and the width of the last scattering surface. Using the recent CMB and SDSS data, we find that the recent data constraints favor the accelerated recombination model, though the other models (standard, delayed recombination) are not ruled out at 1-$\sigma$ confidence level. If the accelerated recombination had actually occurred in our early Universe, baryonic clustering on small-scales is likely to be the cause of it. By comparing the ionization history of baryonic cloud models with that of the best-fit accelerated recombination model, we find that some portion of our early Universe has baryonic underdensity. We have made the forecast on the PLANCK data constraint, which shows that we will be able to rule out the standard or delayed recombination models, if the recombination in our early Universe had proceeded with $\epsilon_\alpha\sim-0.01$ or lower, and residual foregrounds and systematic effects are negligible.Comment: v2: matched with the accepted version (conclusions unchanged