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

Anthony R. Pullen, Marc Kamionkowski

    Research output: Contribution to journalArticle

    Abstract

    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
    Volume76
    Issue number10
    DOIs
    StatePublished - Nov 21 2007

    Fingerprint

    Power Spectrum
    Microwave
    power spectra
    statistics
    Statistics
    microwaves
    estimators
    Dependent
    quadrupoles
    Minimum Variance
    Variance Estimator
    Spherical Harmonics
    Isotropy
    isotropy
    spherical harmonics
    Cosmology
    Inflation
    cosmology
    Anisotropy
    Polarization

    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Nuclear and High Energy Physics
    • Mathematical Physics

    Cite this

    Cosmic microwave background statistics for a direction-dependent primordial power spectrum. / Pullen, Anthony R.; Kamionkowski, Marc.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 76, No. 10, 103529, 21.11.2007.

    Research output: Contribution to journalArticle

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