Linear power spectra in cold+hot dark matter models: analytical approximations and applications

摘要

This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold+hot dark matter (CDM+HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wavenumber, neutrino fraction, redshift, and Hubble constant: k\lo 10\,h Mpc^{-1}, 0.05\lo \onu\lo 0.3, 0\le z\lo 15, and 0.5\lo h \lo 0.8. A new, redshift-dependent shape parameter \Gamma_\nu=a^{1/2}\onu h^2 is introduced to simplify the multi-dimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of \Gamma_\nu lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and \onu. Linear calculations with these power spectra as input are performed to compare the predictions of \onu\lo 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8\lo n\le 1. It is found that a slight tilt of n=0.9 (no tensor mode) or n=0.95 (with tensor mode) in \onu\sim 0.1-0.2 CDM+HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter \Gamma=0.25, providing good agreement with the power spectrum reconstructed by Peacock and Dodds (1994) and the observed cluster abundance.