Search for gravitational waves in the CMB after WMAP3: Foreground confusion and the optimal frequency coverage for foreground minimization

Abstract

$B$-modes of cosmic microwave background (CMB) polarization can be created by a primordial gravitational wave background. If this background was created by inflation, then the amplitude of the polarization signal is proportional to the energy density of the universe during inflation. The primordial signal will be contaminated by polarized foregrounds including dust and synchrotron emission within the galaxy. In light of the WMAP polarization maps, we consider the ability of several hypothetical CMB polarization experiments to separate primordial CMB $B$-mode signal from galactic foregrounds. We also study the optimization of a CMB experiment with a fixed number of detectors in the focal plane to determine how the detectors should be distributed in different frequency bands to minimize foreground confusion. We show that the optimal configuration requires observations in at least 5 channels spread over the frequency range between 30 and 500 GHz with substantial coverage around 150 GHz. If a low-resolution space experiment using 1000 detectors to reach a noise level of about $1000\text{ }\text{ }{\mathrm{nK}}^{2}$ concentrates on roughly 66% of the sky with the least foreground contamination, the minimum detectable level of the tensor-to-scalar ratio would be about 0.002 at the 99% confidence level for an optical depth of 0.1.