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

We develop a model for the matter power spectrum as the sum of Zeldovich approximation and even powers of $k$, i.e., $A_0 - A_2k^2 + A_4k^4 - ...$, compensated at low $k$. With terms up to $k^4$ the model can predict the true power spectrum to a few percent accuracy up to $k\sim 0.7 h \rm{Mpc}^{-1}$, over a wide range of redshifts and models. The $A_n$ 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 $A_0$ variance, which reproduces the simulations remarkably well. In contrast, we show that one needs an N-body simulation volume of more than 1000 $({\rm Gpc}/h)^3$ to converge to 1\% accuracy on covariance matrix. We investigate the super-sample variance effect and show it can be modeled as an additional parameter that can be determined from the data. This allows a determination of $\sigma_8$ amplitude to about 0.2\% for a survey volume of 1$({\rm Gpc}/h)^3$, compared to 0.4\% otherwise. We explore the sensitivity of these coefficients to baryonic effects using hydrodynamic simulations of van Daalen (2011). We find that because of baryons redistributing matter inside halos all the coefficients $A_{2n}$ for $n>0$ are strongly affected by baryonic effects, while $A_0$ 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 $A_0$ and Zeldovich terms.