Approximate Likelihood Approaches for Detecting the Influence of Primordial Gravitational Waves in Cosmic Microwave Background Polarization
arXiv:1709.00102 · doi:10.1103/PhysRevD.97.103512
Abstract
One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio from CMB polarization observations, which combines the benefits of a full-scale likelihood approach with the tractability of the quadratic delensing technique. This method is a pixel space, all order likelihood analysis of the quadratic delensed B modes, and it essentially builds upon the quadratic delenser by taking into account all order lensing and pixel space anomalies. Its tractability relies on a crucial factorization of the pixel space covariance matrix of the polarization observations which allows one to compute the full Gaussian approximate likelihood profile, as a function of , at the same computational cost of a single likelihood evaluation.
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