An analytic approximation of MDM power spectra in four dimensional parameter space

Abstract

An accurate analytic approximation of the transfer function for the power spectra of primordial density perturbations in mixed dark matter models is presented. The fitting formula in a matter-dominated Universe ($Ω_0=Ω_M=1$) is a function of wavenumber $k$, redshift $z$ and four cosmological parameters: the density of massive neutrinos, $Ω_ν$, the number of massive neutrino species, $N_ν$, the baryon density, $Ω_{b}$ and the dimensionless Hubble constant, $h$. Our formula is accurate in a broad range of parameters: $k\le 100 h/Mpc$, $z\le 30$, $Ω_ν\le 0.5$, $N_ν\le 3$, $Ω_{b}\le 0.3$, $0.3\le h\le 0.7$. The deviation of the variance of density fluctuations calculated with our formula from numerical results obtained with CMBfast is less than 6% for the entire range of parameters. It increases with $Ω_bh^{2}$ and is less than $\le 3%$ for $Ω_bh^{2}\le 0.05$. The performance of the analytic approximation of MDM power spectra proposed here is compared with other approximations found in the literature. Our approximation turns out to be closest to numerical results in the parameter space considered here.