Dependence of cosmic shear covariances on cosmology

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.

COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions

“…The covariances used in our likelihood analysis are calculated from the power spectrum P E as described in , assuming our fiducial cosmology. This method does not account for the non-Gaussianity of the shear field or the cosmology-dependence of the covariance (Eifler et al 2009), however these issues are not crucial for our purpose as we are only interested in the relative performance of COSEBIs and the 2PCFs. More important is that we can choose an arbitrary binning in the 2PCF covariance.…”

The removal of shear-ellipticity correlations from the cosmic shear signal

“…Since an additional cosmology dependence would lead to tighter constraints, this is a conservative assumption (see e.g. Eifler et al 2009). Using the equivalence of the Fisher matrices, and returning to the notation in the context of the nulling technique, we then arrive from (25) at the following expression for the original (index "orig") and the nulled (index "null") data vector (see Appendix.…”

Simulations of Baryon Acoustic Oscillations. Ii. Covariance Matrix of the Matter Power Spectrum

“…This non-Gaussian contribution is described by the trispectrum or the Fourier transform of the 4-point correlation function. Cooray & Hu (2001) used the halo model to estimate the trispectrum contribution and showed that the non-Gaussian errors do degrade the precision of cosmological parameter determination, and therefore cannot be ignored for planned future surveys (see also Takada & Jain 2008;Eifler, Schneider & Hartlap 2008). Also recently, Smith (2008) studied the covariance matrix of the halo power spectrum using numerical simulations.…”