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

An accurate analytic approximation of the transfer function for the power s pectra of primordial density perturbations in mixed dark matter models is p resented. The fitting formula in a matter-dominated Universe (Omega(0) = Om ega(M) = 1) is a function of wavenumber k, redshift z and four cosmological parameters: the density of massive neutrinos, Omega(nu), the number of mas sive neutrino species, N-nu, the baryon density, Omega(b) and the dimension less Hubble constant, k. Our formula is accurate in a broad range of parame ters: k less than or equal to 100 h/Mpc, z less than or equal to 30, Omega( nu) less than or equal to 0.5, N-nu less than or equal to 3, Omega(b) less than or equal to 0.3, 0.3 less than or equal to h less than or equal to 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 t he entire range of parameters. It increases with Omega(b)h(2) and is less t han less than or equal to 3% for Omega(b)h(2) less than or equal to 0.05. The performance of the analytic approximation of MDM power spectra proposed here is compared with other approximations found in the literature (Holtzm an 1989; Pogosyan & Starobinsky 1995; Ma 1996; Eisenstein & Hu 1997b). Our approximation turns out to be closest to numerical results in the parameter space considered here.