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

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

2007-01-31

arxiv.org/abs/astro-ph/0701921v1

Astrophys.J.664:680-686, 2007

Astronomy and Astrophysics

Astrophysics

Submitted to Apj

Scientific paper

10.1086/519071

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 Cramer 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 speed-up 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. Our estimator in its current form is optimal if noise is homogeneous. In future work our fast polarized bispectrum estimator should be extended to deal with inhomogeneous noise in an analogous way to how the existing fast temperature estimator was generalized.

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