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Published November 15, 2007 | Published
Journal Article Open

Cosmic microwave background statistics for a direction-dependent primordial power spectrum


Statistical isotropy of primordial perturbations is a common assumption in cosmology, but it is an assumption that should be tested. To this end, we develop cosmic microwave background statistics for a primordial power spectrum that depends on the direction, as well as the magnitude, of the Fourier wave vector. We first consider a simple estimator that searches in a model-independent way for anisotropy in the square of the temperature (and/or polarization) fluctuation. We then construct the minimum-variance estimators for the coefficients of a spherical-harmonic expansion of the directional dependence of the primordial power spectrum. To illustrate, we apply these statistics to an inflation model with a quadrupole dependence of the primordial power spectrum on direction and find that a power quadrupole as small as 2.0% can be detected with the Planck satellite.

Additional Information

© 2007 The American Physical Society. (Received 7 September 2007; published 21 November 2007) We thank D. Babich, K. Gorski, M. Wise, and C. Pahud for useful comments on an earlier draft. M.K. acknowledges the hospitality of the Aspen Center for Physics, where part of this work was completed. A.P. acknowledges the support of the NSF. This work was supported by DOE DE-FG03-92-ER40701, NASA NNG05GF69G, the Gordon and Betty Moore Foundation, and a NASA Einstein Probe mission study grant, "The Experimental Probe of Inflationary Cosmology."

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