### Abstract

A central assumption in our analysis of cosmic structure is that cosmological perturbations have a constant ensemble mean, which can be set to zero by appropriate choice of the background. This property is one of the consequences of statistical homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which primordial perturbations have inhomogeneous non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, our test does not make any additional assumptions about the nature of the perturbations and is thus rather generic and model-independent. The test statistic we employ is essentially Student's t statistic, applied to appropriately masked, foreground-cleaned cosmic microwave background anisotropy maps produced by the WMAP mission. We find evidence for a non-zero mean in a particular range of multipoles, but the evidence against the zero mean hypothesis goes away when we correct for multiple testing. We also place constraints on the mean of the temperature multipoles as a function of angular scale. On angular scales smaller than four degrees, a non-zero mean has to be at least an order of magnitude smaller than the standard deviation of the temperature anisotropies.

Original language | English (US) |
---|---|

Article number | 048 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2011 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2011 |

### Fingerprint

### Keywords

- cosmological parameters from CMBR
- cosmological perturbation theory
- physics of the early universe

### ASJC Scopus subject areas

- Astronomy and Astrophysics

### Cite this

*Journal of Cosmology and Astroparticle Physics*,

*2011*(3), [048]. https://doi.org/10.1088/1475-7516/2011/03/048

**Do cosmological perturbations have zero mean?** / Armendariz-Picon, Cristian.

Research output: Contribution to journal › Article

*Journal of Cosmology and Astroparticle Physics*, vol. 2011, no. 3, 048. https://doi.org/10.1088/1475-7516/2011/03/048

}

TY - JOUR

T1 - Do cosmological perturbations have zero mean?

AU - Armendariz-Picon, Cristian

PY - 2011/3

Y1 - 2011/3

N2 - A central assumption in our analysis of cosmic structure is that cosmological perturbations have a constant ensemble mean, which can be set to zero by appropriate choice of the background. This property is one of the consequences of statistical homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which primordial perturbations have inhomogeneous non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, our test does not make any additional assumptions about the nature of the perturbations and is thus rather generic and model-independent. The test statistic we employ is essentially Student's t statistic, applied to appropriately masked, foreground-cleaned cosmic microwave background anisotropy maps produced by the WMAP mission. We find evidence for a non-zero mean in a particular range of multipoles, but the evidence against the zero mean hypothesis goes away when we correct for multiple testing. We also place constraints on the mean of the temperature multipoles as a function of angular scale. On angular scales smaller than four degrees, a non-zero mean has to be at least an order of magnitude smaller than the standard deviation of the temperature anisotropies.

AB - A central assumption in our analysis of cosmic structure is that cosmological perturbations have a constant ensemble mean, which can be set to zero by appropriate choice of the background. This property is one of the consequences of statistical homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which primordial perturbations have inhomogeneous non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, our test does not make any additional assumptions about the nature of the perturbations and is thus rather generic and model-independent. The test statistic we employ is essentially Student's t statistic, applied to appropriately masked, foreground-cleaned cosmic microwave background anisotropy maps produced by the WMAP mission. We find evidence for a non-zero mean in a particular range of multipoles, but the evidence against the zero mean hypothesis goes away when we correct for multiple testing. We also place constraints on the mean of the temperature multipoles as a function of angular scale. On angular scales smaller than four degrees, a non-zero mean has to be at least an order of magnitude smaller than the standard deviation of the temperature anisotropies.

KW - cosmological parameters from CMBR

KW - cosmological perturbation theory

KW - physics of the early universe

UR - http://www.scopus.com/inward/record.url?scp=79953666053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953666053&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2011/03/048

DO - 10.1088/1475-7516/2011/03/048

M3 - Article

AN - SCOPUS:79953666053

VL - 2011

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 3

M1 - 048

ER -