Non-Gaussian covariance of CMB B modes of polarization and parameter degradation

The B-mode polarization lensing signal is a useful probe of the neutrino mass and to a lesser extent the dark energy equation of state as the signal depends on the integrated mass power spectrum between us and the last scattering surface. This lensing B-mode signal, however, is non-Gaussian and the resulting non-Gaussian covariance to the power spectrum could impact cosmological parameter measurements, as correlations between B-mode bins are at a level of 0.1. On the other hand, for temperature and E-mode polarization power spectra, the non-Gaussian covariance is not significant, where we find correlations at the 10(-5) level even for adjacent bins. When the power spectrum is estimated with roughly 5 uniformly spaced bins from l = 5 to l = 100 and 13 logarithmic uniformly spaced bins from l = 100 to l = 2000, the resulting degradation on neutrino mass and dark energy equation of state is about a factor of 2 to 3 when compared to the case where statistics are simply considered to be Gaussian. If we increase the total number of bins between l = 5 and l = 2000 to be about 100, we find that the non-Gaussianities only make a minor difference with less than a few percent correction to uncertainties of most cosmological parameters determined from the data. For Planck, the resulting constraints on the sum of the neutrino masses is sigma(Sigma m nu)similar to 0.2 eV and on the dark energy equation of state parameter we find that sigma(w)similar to 0.5. A post-Planck experiment can improve the neutrino mass measurement by a factor of 3 to 4.