### Abstract

Context. In cosmic shear likelihood analyses, the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not influence the likelihood contours. Aims. We examine whether the aforementioned assumptions hold and quantify how strong cosmic shear covariances vary within a reasonable parameter range. Furthermore, we examine the impact on likelihood, contours when, assuming different cosmologies in the covariance. The final goal is to develop an improved likelihood analysis for parameter estimation with cosmic shear. Methods. We calculate Gaussian covariances analytically for 2500 different cosmologies. To quantify the impact on the parameter constraints, we perform a likelihood analysis for each covariance matrix and compare the likelihood contours. To improve on the assumption of a constant covariance, we use an adaptive covariance matrix, which is continuously updated according to the point in parameter space where the likelihood is evaluated. As a side-effect, this cosmology-dependent covariance improves the parameter constraints. We examine this more closely using the Fisher-matrix formalism. In addition, we quantify the impact of non-Gaussian covariances on the likelihood contours using a ray-tracing covariance derived from the Millennium simulation. In this ansatz, we return to the approximation of a cosmology-independent covariance matrix, and to minimize the error due to this approximation, we develop the concept of an iterative likelihood analysis. Results. Covariances vary significantly within the considered parameter range. The cosmology assumed in the covariance has a nonnegligible impact on the size of the likelihood contours. This impact increases with increasing survey size, increasing number density of source galaxies, decreasing ellipticity noise, and when taking non-Gaussianity into account. A proper treatment of this effect is therefore even more important for future surveys. In this paper, we present methods for taking cosmology-dependent covariances into account.

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

Pages (from-to) | 721-731 |

Number of pages | 11 |

Journal | Astronomy and astrophysics |

Volume | 502 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cosmology: Cosmological parameters
- Cosmology: Large-scale structure of the Universe
- Cosmology: Theory
- Methods: Statistical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astronomy and astrophysics*,

*502*(3), 721-731. https://doi.org/10.1051/0004-6361/200811276

**Dependence of cosmic shear covariances on cosmology impact on parameter estimation.** / Eifler, T.; Schneider, P.; Hartlap, J.

Research output: Contribution to journal › Article

*Astronomy and astrophysics*, vol. 502, no. 3, pp. 721-731. https://doi.org/10.1051/0004-6361/200811276

}

TY - JOUR

T1 - Dependence of cosmic shear covariances on cosmology impact on parameter estimation

AU - Eifler, T.

AU - Schneider, P.

AU - Hartlap, J.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - Context. In cosmic shear likelihood analyses, the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not influence the likelihood contours. Aims. We examine whether the aforementioned assumptions hold and quantify how strong cosmic shear covariances vary within a reasonable parameter range. Furthermore, we examine the impact on likelihood, contours when, assuming different cosmologies in the covariance. The final goal is to develop an improved likelihood analysis for parameter estimation with cosmic shear. Methods. We calculate Gaussian covariances analytically for 2500 different cosmologies. To quantify the impact on the parameter constraints, we perform a likelihood analysis for each covariance matrix and compare the likelihood contours. To improve on the assumption of a constant covariance, we use an adaptive covariance matrix, which is continuously updated according to the point in parameter space where the likelihood is evaluated. As a side-effect, this cosmology-dependent covariance improves the parameter constraints. We examine this more closely using the Fisher-matrix formalism. In addition, we quantify the impact of non-Gaussian covariances on the likelihood contours using a ray-tracing covariance derived from the Millennium simulation. In this ansatz, we return to the approximation of a cosmology-independent covariance matrix, and to minimize the error due to this approximation, we develop the concept of an iterative likelihood analysis. Results. Covariances vary significantly within the considered parameter range. The cosmology assumed in the covariance has a nonnegligible impact on the size of the likelihood contours. This impact increases with increasing survey size, increasing number density of source galaxies, decreasing ellipticity noise, and when taking non-Gaussianity into account. A proper treatment of this effect is therefore even more important for future surveys. In this paper, we present methods for taking cosmology-dependent covariances into account.

AB - Context. In cosmic shear likelihood analyses, the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not influence the likelihood contours. Aims. We examine whether the aforementioned assumptions hold and quantify how strong cosmic shear covariances vary within a reasonable parameter range. Furthermore, we examine the impact on likelihood, contours when, assuming different cosmologies in the covariance. The final goal is to develop an improved likelihood analysis for parameter estimation with cosmic shear. Methods. We calculate Gaussian covariances analytically for 2500 different cosmologies. To quantify the impact on the parameter constraints, we perform a likelihood analysis for each covariance matrix and compare the likelihood contours. To improve on the assumption of a constant covariance, we use an adaptive covariance matrix, which is continuously updated according to the point in parameter space where the likelihood is evaluated. As a side-effect, this cosmology-dependent covariance improves the parameter constraints. We examine this more closely using the Fisher-matrix formalism. In addition, we quantify the impact of non-Gaussian covariances on the likelihood contours using a ray-tracing covariance derived from the Millennium simulation. In this ansatz, we return to the approximation of a cosmology-independent covariance matrix, and to minimize the error due to this approximation, we develop the concept of an iterative likelihood analysis. Results. Covariances vary significantly within the considered parameter range. The cosmology assumed in the covariance has a nonnegligible impact on the size of the likelihood contours. This impact increases with increasing survey size, increasing number density of source galaxies, decreasing ellipticity noise, and when taking non-Gaussianity into account. A proper treatment of this effect is therefore even more important for future surveys. In this paper, we present methods for taking cosmology-dependent covariances into account.

KW - Cosmology: Cosmological parameters

KW - Cosmology: Large-scale structure of the Universe

KW - Cosmology: Theory

KW - Methods: Statistical

UR - http://www.scopus.com/inward/record.url?scp=68649119573&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68649119573&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/200811276

DO - 10.1051/0004-6361/200811276

M3 - Article

AN - SCOPUS:68649119573

VL - 502

SP - 721

EP - 731

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

IS - 3

ER -