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We develop a model for the matter power spectrum as the sum of Zeldovichapproximation 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 truepower 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 containinformation about cosmology, in particular amplitude of fluctuations. We writea simple form of the covariance matrix as a sum of Gaussian part and $A_0$variance, which reproduces the simulations remarkably well. In contrast, weshow that one needs an N-body simulation volume of more than 1000 $({\rmGpc}/h)^3$ to converge to 1\% accuracy on covariance matrix. We investigate thesuper-sample variance effect and show it can be modeled as an additionalparameter 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 coefficientsto baryonic effects using hydrodynamic simulations of van Daalen (2011). Wefind that because of baryons redistributing matter inside halos all thecoefficients $A_{2n}$ 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 canbe effectively marginalized over the baryonic effects, while still preservingthe bulk of the cosmological information contained in $A_0$ and Zeldovichterms.

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