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Published July 1, 2013 | Published
Journal Article Open

Primordial Gravitational Wave Detectability with Deep Small-sky Cosmic Microwave Background Experiments

Abstract

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.

Additional Information

© 2013 American Astronomical Society. Received 2011 August 7; accepted 2013 April 22; published 2013 June 10. We thank our many Spider, ABS, and Planck collaborators for many stimulating discussions about the experimental assault on CMB tensor mode detection. We thank William C. Jones for his helpful comments on the text. We thank Marc Antoine Miville Deschênes for advice and aid on foregrounds. Support from NSERC, the Canadian Institute for Advanced Research, and the Canadian Space Agency (for PlanckHFI and Spider work) is gratefully acknowledged. Part of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The large matrix computations were performed using the SciNET facility at the University of Toronto. Some of the results in this paper have been derived using the HEALPix package (Górski et al. 2005), http://healpix.jpl.nasa.gov.

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