A Bayesian ILC method for CMB B-mode posterior estimation and
  reconstruction of primordial gravity wave signal
  The Cosmic Microwave Background (CMB) radiation B mode polarization signal
contains the unique signature of primordial metric perturbations produced
during the inflation. The separation of the weak CMB B-mode signal from strong
foreground contamination in observed maps is a complex task, and proposed new
generation low noise satellite missions compete with the weak signal level of
this gravitational background. In this article, for the first time, we employ a
foreground model-independent internal linear combination (ILC) method to
reconstruct the CMB B mode signal using simulated observations over large
angular scales of the sky of 6 frequency bands of future generation CMB mission
Probe of Inflation and Cosmic Origins (PICO). We estimate the joint CMB B mode
posterior density following the interleaving Gibbs steps of B mode angular
power spectrum and cleaned map samples using the ILC method. We extend and
improve the earlier reported Bayesian ILC method to analyze weak CMB B mode
reconstruction by introducing noise bias corrections at two stages during the
ILC weight estimation. By performing $200$ Monte Carlo simulations of the
Bayesian ILC method, we find that our method can reconstruct the CMB signals
and the joint posterior density accurately over large angular scales of the
sky. We estimate Blackwell-Rao statistics of the marginal density of CMB B mode
angular power spectrum and use them to estimate the joint density of scalar to
tensor ratio $r$ and a lensing power spectrum amplitude $A^{\textrm{lens}}$.
Using $200$ Monte Carlo simulations of the delensing approach, we find that our
method can achieve an unbiased detection of the primordial gravitational wave
signal $r$ with more than 8$\sigma$ significance for levels of $r \geqslant
0.01$.
