Precision of future experiments measuring primordial tensor fluctuation

Abstract

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. We forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements, with $n_{\rm t}$ as a free parameter, from a {\it Planck}-like experiment, and from Spider and POLARBEAR given the current understanding of their experimental noise and foreground contamination. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.