Cosmic microwave background constraints on the tensor-to-scalar ratio

One of the main goals of modern cosmic microwave background (CMB) missions is to measure the tensor-to-scalar ratio r accurately to constrain inflation models. Due to ignorance about the reionization history X_e(z), this analysis is usually done by assuming an instantaneous reionization X_e(z) which, however, can bias the best-fit value of r. Moreover, due to the strong mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying the sky coverage fraction f_sky by the full-sky likelihood would not give satisfactory results. In this work, we forecast constraints on r for the Planck mission taking into account the general reionization scenario and cut-sky effects. Our results show that by applying an N-point interpolation analysis to the reionization history, the bias induced by the assumption of instantaneous reionization is removed and the value of r is constrained within 5% error level, if the true value of r is greater than about 0.1.