The bulk of recent cosmological research has focused on the adiabatic cold dark matter model and its simple extensions. Here we present an accurate fitting formula that describes the matter transfer functions of all common variants, including mixed dark matter models. The result is a function of wavenumber, time, and six cosmological parameters: the massive neutrino density, number of neutrino species degenerate in mass, baryon density, Hubble constant, cosmological constant, and spatial curvature. We show how observational constraints—e.g., the shape of the power spectrum, the abundance of clusters and damped Lyα systems, and the properties of the Lyα forest—can be extended to a wide range of cosmologies, which includes variations in the neutrino and baryon fractions in both high-density and low-density universes.
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