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General solution to the E−B mixing problem

Kendrick M. Smith1,2 and Matias Zaldarriaga3,4

  • 1Kavli Institute for Cosmological Physics, Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
  • 2Department of Physics, University of Chicago, 60637
  • 3Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 4Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA

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Phys. Rev. D 76, 043001 – Published 2 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.043001

Abstract

We derive a general ansatz for optimizing pseudo-Cℓ estimators used to measure cosmic microwave background anisotropy power spectra, and apply it to the recently proposed pure pseudo-Cℓ formalism, to obtain an estimator which achieves near-optimal B-mode power spectrum errors for any specified noise distribution while minimizing leakage from ambiguous modes. Our technique should be relevant for upcoming cosmic microwave background polarization experiments searching for B-mode polarization. We compare our technique both to the theoretical limits based on a full Fisher matrix calculation and to the standard pseudo-Cℓ technique. We demonstrate it by applying it to a fiducial survey with realistic inhomogeneous noise, complex boundaries, point source masking, and a noise level comparable to what is expected for next-generation experiments (∼5.75  μK−arcmin). For such an experiment our technique could improve the constraints on the amplitude of a gravity wave background by over a factor of 10 compared to what could be obtained using ordinary pseudo-Cℓ, coming quite close to saturating the theoretical limit. Constraints on the amplitude of the lensing B-modes are improved by about a factor of 3.

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Phys. Rev. D 76, 043001– Published 2 August, 2007
  • Received 10 December 2006

© 2007 American Physical Society

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