### 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 language | English (US) |
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Article number | 103529 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 76 |

Issue number | 10 |

DOIs | |

State | Published - Nov 21 2007 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*76*(10), [103529]. https://doi.org/10.1103/PhysRevD.76.103529

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

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 76, no. 10, 103529. https://doi.org/10.1103/PhysRevD.76.103529

}

TY - JOUR

T1 - Cosmic microwave background statistics for a direction-dependent primordial power spectrum

AU - Pullen, Anthony R.

AU - Kamionkowski, Marc

PY - 2007/11/21

Y1 - 2007/11/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36349004043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36349004043&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.76.103529

DO - 10.1103/PhysRevD.76.103529

M3 - Article

AN - SCOPUS:36349004043

VL - 76

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 10

M1 - 103529

ER -