Limits on the detectability of the CMB B-mode polarization imposed by foregrounds

We investigate which practical constraints are imposed by foregrounds on the detection of the B-mode polarization generated by gravitational waves, in the case of experiments of the type currently being planned. As the B-mode signal is probably dominated by foregrounds at all frequencies, the detection of the cosmological component depends drastically on our ability to remove foregrounds. We provide an analytical expression with which to estimate the level of the residual polarization for Galactic foregrounds, according to the method employed for their subtraction. We interpret this result in terms of the lower limit of the tensor-to-scalar ratio r that allows us to disentangle the cosmological B-mode polarization from the foreground contribution. Polarized emission from extragalactic radio sources and gravitational lensing is also taken into account. As a first approach, we consider the ideal limit of an instrumental noise-free experiment: for full-sky coverage and a resolution of 1 degrees, we obtain a limit of r similar to 10(-4). This value can be improved by high-resolution experiments and, in principle, there is no clear fundamental limit on the detectability of the polarization of gravitational waves. Our analysis is also applied to planned or hypothetical future polarization experiments, taking into account expected noise levels.