Detectability of tensor modes in the presence of foregrounds

In inflationary models, gravitational waves are produced and generate B-type polarization in the CMB. Since B polarization is only generated by gravity waves it does not suffer from the cosmic variance. A perfect decomposition of the CMB into B-modes and E-modes would require data from the entire sky, which in practice is not possible because of the foreground contaminants. This leads to mixing of E polarization into B, which introduces cosmic variance conta- mination of B polarization and reduces sensitivity to gravity wave amplitude even in absence of detector noise. We present numerical results for the uncertainty in the tensor-to-scalar ratio using the Fisher matrix formalism for various resolutions, using foreground models based on dust maps and assuming 90 GHz operating frequency. We find that the usual scaling delta(T/S) ~ f_sky^(-1/2) is significantly degraded and becomes delta(T/S) ~ f_sky^(-2) for f_sky>0.7. This dependence is affected only weakly by the choice of sky cuts. To achieve a T/S=10^(-3) detection at 3 sigma one needs to observe 15% of the sky as opposed to naive expectation of 0.3%. To prevent contamination over this large sky area at required level one must be able to remove polarized dust emission at or better than 0.1% of unpolarized intensity, assuming the cleanest part of the sky has been chosen. To achieve T/S=10^(-4) detection at 3 sigma one needs to observe 70% of the sky, which is only possible if dust emission is removed everywhere over this region at 0.01% level. Reaching T/S=10^(-2) should be easier: 1% of the sky is needed over which polarized emission needs to be removed at 1% of total intensity if the cleanest region is chosen. These results suggest that foreground contamination may make it difficult to achieve levels below T/S=10^(-3). (abridged)