Analytic model for the matter power spectrum, its covariance matrix and baryonic effects

Abstract

We develop a model for the matter power spectrum as the sum of Zeldovich approximation and even powers of k, i.e. A0 - A2k2 + A4k4 - . . . , compensated at low k. With terms up to k4, the model can predict the true power spectrum to a few per cent accuracy up to k ~ 0.7 h Mpc-1, over a wide range of redshifts and models. The An coefficients contain information about cosmology, in particular amplitude of fluctuations. We write a simple form of the covariance matrix as a sum of Gaussian part and A0 variance, which reproduces the simulations remarkably well. In contrast, we show that one needs an N-body simulation volume of more than 1000 (Gpc h-1)3 to converge to 1 per cent accuracy on covariance matrix. We investigate the supersample variance effect and show it can be modelled as an additional parameter that can be determined from the data. This allows a determination of σ8 amplitude to about 0.2 per cent for a survey volume of 1(Gpc h-1)3, compared to 0.4 per cent otherwise.We explore the sensitivity of these coefficients to baryonic effects using hydrodynamic simulations of van Daalen et al. We find that because of baryons redistributing matter inside haloes all the coefficients A2n for n > 0 are strongly affected by baryonic effects, while A0 remains almost unchanged, a consequence of halo mass conservation. Our results suggest that observations such as weak lensing power spectrum can be effectively marginalized over the baryonic effects, while still preserving the bulk of the cosmological information contained in 0 and Zeldovich terms.