Reionization and CMB non-Gaussianity

16 pages, 8 figures; MNRAS in pressInternational audienceWe show how cross-correlating a high redshift external tracer field, such as the 21cm neutral hydrogen distribution and product maps involving Cosmic Microwave Background (CMB) temperature and polarisation fields, that probe mixed bispectrum involving these fields, can help to determine the reionization history of the Universe, beyond what can be achieved from cross-spectrum analysis. Taking clues from recent studies for the detection of primordial non-Gaussianity (Munshi & Heavens 2010), we develop a set of estimators that can study reionization using a power spectrum associated with the bispectrum (or skew-spectrum). We use the matched filtering inherent in this method to investigate different reionization histories. We check to what extent they can be used to rule out various models of reionization and study cross contamination from different sources such as the lensing of the CMB. The estimators can be fine-tuned to optimize study of a specific reionization history. We consider three different types of tracers in our study, namely: proto-galaxies; 21cm maps of neutral hydrogen; quasars. We also consider four alternative models of reionization. We find that the cumulative signal-to-noise (S/N) for detection at $\ell_{max}=2000$ can reach $\mathcal{O}(70)$ for cosmic variance limited all-sky experiments. Combining 100GHz, 143GHz and 217GHz channels of the Planck experiment, we find that the (S/N) lies in the range $\mathcal{O}(5)-\mathcal{O}(35)$. The (S/N) depends on the specific choice of a tracer field, and multiple tracers can be effectively used to map out the entire reionization history with reasonable S/N. Contamination from weak lensing is investigated and found to be negligible, and the effects of Thomson scattering from patchy reionizationare also considered