Abstract
Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.
Highlights
We are entering a phase in which cosmological galaxy surveys will have remarkable constraining power
Before we study the importance of the parameter dependence in the covariance matrix in detail for the case of tomographic large-scale structure datasets, let us examine a simpler scenario: a single sky map, and a single parameter quantifying the overall amplitude of the power spectrum
In the era of precision cosmology it is becoming increasingly important to understand the systematic and statistical errors that occur during parameter estimation
Summary
We are entering a phase in which cosmological galaxy surveys will have remarkable constraining power. Our aim is to quantify the impact on parameter estimation of including (or not) the parameter dependence of the covariance matrix for upcoming photometric redshift surveys Previous work on this topic has focused on the Fisher information of a parameterdependent covariance in the two-point likelihood of Gaussian random fields [34], and on the overall parameter dependence of the cosmic shear two-point covariance [35], where the authors quantified the effect on the likelihood contours of σ8 and Ωm, using both analytic and ray tracing simulations.
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