Fast Estimator of Primordial Non‐Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background

Measurements of primordial non-Gaussianity ( f NL ) open a new window onto the physics of inflation. We describe a fast cubic (bispectrum) estimator of f NL , using a combined analysis of temperature and polarization observations. The speed of our estimator allows us to use a sufficient number of Monte Carlo simulations to characterize its statistical properties in the presence of real-world issues such as instrumental effects, partial sky coverage, and foreground contamination. We find that our estimator is optimal, where optimality is defined by saturation of the Cramér-Rao bound, if noise is homogeneous. Our estimator is also computationally efficient, scaling as O ( N 3/2 ), compared to the O ( N 5/2 ) scaling of the brute-force bispectrum calculation for sky maps with N pixels. For Planck this translates into a speedup by factors of millions, reducing the required computing time from thousands of years to just hours and thus making f NL estimation feasible for future surveys.