Revising the Halofit Model for the Nonlinear Matter Power Spectrum

Abstract

Based on a suite of state-of-the-art high-resolution N -body simulations, we revisit the so-called halofit model (Smith et al. 2003) as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has been frequently used as a standard cosmological tool to predict the nonlinear matter power spectrum in a universe dominated by cold dark matter, its precision has been limited by the low-resolution of N -body simulations used to determine the fitting parameters, suggesting the necessity of improved fitting formula at small scales for future cosmological studies. We run high-resolution N -body simulations for 16 cosmological models around the Wilkinson Microwave Anisotropy Probe (WMAP) best-fit cosmological parameters (1, 3, 5, and 7 year results), including dark energy models with a constant equation of state. The simulation results are used to re-calibrate the fitting parameters of the halofit model so as to reproduce small-scale power spectra of the Nbody simulations, while keeping the precision at large scales. The revised fitting formula provides an accurate prediction of the nonlinear matter power spectrum in a wide range of wavenumber (k ≤ 30h Mpc −1 ) at redshifts 0 ≤ z ≤ 10, with 5% precision for k ≤ 1 h Mpc −1 at 0 ≤ z ≤ 10 and 10% for 1 ≤ k ≤ 10 h Mpc −1 at 0 ≤ z ≤ 3. We discuss the impact of the improved halofit model on weak lensing power spectra and correlation functions, and show that the improved model better reproduces ray-tracing simulation results. Subject headings: cosmology: theory -large-scale structure of universe -methods: N-body simulations

The MICE Grand Challenge light-cone simulation – III. Galaxy lensing mocks from all-sky lensing maps

“…This is consistent with a similar analysis from the higher-resolution Millennium Simulation (Hilbert et al 2009). On the other hand, other recent high-resolution simulations seem to find an even larger power excess at this highly non-linear scales (see Takahashi et al (2012)). …”

Cosmic discordance: are Planck CMB and CFHTLenS weak lensing measurements out of tune?

“…For this work the modules were: camb (Lewis et al 2000), to calculate CMB and linear matter power spectra and expansion histories; Halofit for non-linear power; a module based on cosmocalc 1 to compute cosmic shear spectra and intrinsic alignments; a custom module to compute the 2-point shear correlation functions ξ±(θ) from C ; the commander, lowlike and CAMSpec Planck likelihood codes (Planck collaboration et al 2013); and a custom CFHTLenS likelihood code. As a default we use the Halofit formulation as implemented by camb, which is Takahashi et al (2012) with modified massive neutrino parameters (although we compare this nonlinear correction to others in Section 3.2). We'll refer to this implementation as TA12 from now on.…”

Joint measurement of lensing–galaxy correlations using SPT and DES SV data

“…A common prescription is Halofit (Smith et al 2003), which calibrates the nonlinear matter power spectrum using dark matter-only N-body simulations. Here we use the updated Halofit model from Takahashi et al (2012). Although Halofit has been shown to accurately reproduce the galaxy power spectrum at moderately nonlinear scales 6 http://camb.info (e.g.…”