Measuring the tensor to scalar ratio from CMB B-modes in the presence of foregrounds

Aims. We investigate the impact of polarised foreground emission on the performances of future CMB experiments aiming to detect primordial tensor fluctuations in the early universe. In particular, we study the accuracy that can be achieved in measuring the tensor-to-scalar ratio r in the presence of foregrounds. Methods. We designed a component separation pipeline, based on the Smica method, aimed at estimating r and the foreground contamination from the data with no prior assumption on the frequency dependence or spatial distribution of the foregrounds. We derived error bars accounting for the uncertainty on foreground contribution. We used the current knowledge of galactic and extragalactic foregrounds as implemented in the Planck sky model (PSM) to build simulations of the sky emission. We applied the method to simulated observations of this modelled sky emission, for various experimental setups. Instrumental systematics are not considered in this study. Results. Our method, with Planck data, permits us to detect r = 0.1 from B-modes only at more than 3 sigma. With a future dedicated space experiment, such as EPIC, we can measure r = 0.001 at similar to 6 sigma for the most ambitious mission designs. Most of the sensitivity to r comes from scales 20 <= l <= 150 for high r values, shifting to lower l's for progressively smaller r. This shows that large-scale foreground emission does not prevent proper measurement of the reionisation bump for full sky experiments. We also investigate the observation of a small but clean part of the sky. We show that diffuse foregrounds remain a concern for a sensitive ground-based experiment with a limited frequency coverage when measuring r < 0.1. Using the Planck data as additional frequency channels to constrain the foregrounds in such ground-based observations reduces the error by a factor two but does not allow detection of r = 0.01. An alternate strategy, based on a deep field space mission with a wide frequency coverage, would allow us to deal with diffuse foregrounds efficiently, but is in return quite sensitive to lensing contamination. In contrast, we show that all-sky missions are nearly insensitive to small-scale contamination (point sources and lensing) if the statistical contribution of such foregrounds can be modelled accurately. Our results do not significantly depend on the overall level and frequency dependence of the diffused foreground model, when varied within the limits allowed by current observations.