Precision modelling of the matter power spectrum in a Planck-like Universe

Abstract

We use a suite of high-resolution $N$-body simulations and state-of-the-art perturbation theory to improve the code halofit, which predicts the nonlinear matter power spectrum. We restrict attention to parameters in the vicinity of the Planck Collaboration's best fit. On large-scales ($k\lesssim 0.07 h/{\rm Mpc}$), our model evaluates the 2-loop calculation from the Multi-point Propagator Theory of Bernardeau et al.(2012). On smaller scales ($k \gtrsim 0.7 h/{\rm Mpc}$), we transition to a smoothing-spline-fit model, that characterises the differences between the Takahashi et al. (2012) recalibration of halofit2012 and our simulations. We use an additional suite of simulations to explore the response of the power spectrum to variations in the cosmological parameters. In particular, we examine: the time evolution of the dark energy equation of state ($w_0$, $w_a$); the matter density $\Omega_m$; the physical densities of CDM and baryons $(\omega_c,\omega_b)$; and the primordial power spectrum amplitude $A_s$, spectral index $n_s$, and its running $\alpha$. We construct correction functions, which improve halofit's dependence on cosmological parameters. Our newly calibrated model reproduces all of our data with $\lesssim1\%$ precision. Including various systematic errors, such as choice of $N$-body code, resolution, and through inspection of the scaled second order derivatives, we estimate the accuracy to be $\lesssim3\%$ over the hyper-cube: $w_0\in\{-1.05,-0.95\}$, $w_a\in\{-0.4,0.4\}$, $\Omega_{\rm m,0}\in\{0.21,0.4\}$, $\omega_{\rm c}\in\{0.1,0.13\}$, $\omega_{\rm b}\in\{2.0,2.4\}$, $n_{\rm s}\in\{0.85,1.05\}$, $A_s\in\{1.72\times 10^{-9},2.58\times 10^{-9}\}$, $\alpha\in\{-0.2,0.2\}$ up to $k=9.0 h/{\rm Mpc}$ and out to $z=3$. Outside of this range the model reverts to halofit2012.