Primordial Gravitational Wave Detectability With Deep Small-Sky Cosmic Microwave Background Experiments

We use the Bayesian estimation on direct T - Q - U cosmic microwave background (CMB) polarization maps to forecast errors on the tensor-to-scalar power ratio r, and hence on primordial gravitational waves, as a function of sky coverage f_sky. This map-based likelihood filters the information in the pixel-pixel space into the optimal combinations needed for r detection for cut skies, providing enhanced information over a first-step linear separation into a combination of E, B, and mixed modes, and ignoring the latter. With current computational power and for typical resolutions appropriate for r detection, the large matrix inversions required are accurate and fast. Our simulations explore two classes of experiments, with differing bolometric detector numbers, sensitivities, and observational strategies. One is motivated by a long duration balloon experiment like Spider, with pixel noise ∝ √f_sky for a specified observing period. This analysis also applies to ground-based array experiments. We find that, in the absence of systematic effects and foregrounds, an experiment with Spider-like noise concentrating on f_sky ~ 0.02-0.2 could place a 2σ_r ≈ 0.014 boundary (~95% confidence level), which rises to 0.02 with an ℓ-dependent foreground residual left over from an assumed efficient component separation. We contrast this with a Planck-like fixed instrumental noise as f_sky varies, which gives a Galaxy-masked (f_sky = 0.75) 2σ_r ≈ 0.015, rising to ≈0.05 with the foreground residuals. Using as the figure of merit the (marginalized) one-dimensional Shannon entropy of r, taken relative to the first 2003 WMAP CMB-only constraint, gives –2.7 bits from the 2012 WMAP9+ACT+SPT+LSS data, and forecasts of –6 bits from Spider (+ Planck); this compares with up to –11 bits for CMBPol, COrE, and PIXIE post-Planck satellites and –13 bits for a perfectly noiseless cosmic variance limited experiment. We thus confirm the wisdom of the current strategy for r detection of deeply probed patches covering the f_sky minimum-error trough with balloon and ground experiments.