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

Anthony R. Pullen, Marc Kamionkowski

    Research output: Contribution to journalArticle


    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.

    Original languageEnglish (US)
    Article number103529
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Issue number10
    StatePublished - Nov 21 2007


    ASJC Scopus subject areas

    • Nuclear and High Energy Physics
    • Physics and Astronomy (miscellaneous)

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