The non-Gaussian matter power spectrum covariance in the halo model approach

Abstract

<p>Weak gravitational lensing is one of the most promising tools to analyze the nature of dark energy and dark matter. In order to constrain cosmological parameters with this method a good theoretical understanding of the underlying dark matter density field is necessary. This work provides an analytical treatment of higher-order correlation functions in the dark matter density field and compares the results obtained with numerical N-body simulations. The tool of choice is a semi-analytic halo model which combines results from perturbation theory and N-body simulations. The main emphasis of this work is on the fourth-order correlation function and its Fourier counterpart, the trispectrum, since it allows us to study the non-Gaussianities of the dark matter field and to calculate the full non-Gaussian covariance of the power spectrum. This provides a way to estimate the error and mode coupling in the dark matter power spectrum to higher accuracy than has been previously.<br /> After deriving an analytical expression for the expectation value of the three-dimensional and the convergence power spectrum covariance, we use the halo model to make explicit predictions for different cosmological models. Additionally, we analyze the impact of a stochastic concentration parameter on the non-Gaussian contribution to the power spectrum covariance. To minimize the computational effort to calculate the full non-Gaussian covariance, different approximations are studied within the halo model approach, and a fitting formula is derived that allows instant calculation of the convergence power spectrum covariance over a wide range of cosmological parameters.</p>