Small‐Scale Perturbations in a General Mixed Dark Matter Cosmology

For a universe with massive neutrinos, cold dark matter, and baryons, wesolve the linear perturbation equations analytically in the small-scale limitand find agreement with numerical codes at the 1-2% level. The inclusion ofbaryons, a cosmological constant, or spatial curvature reduces the small-scalepower and tightens limits on the neutrino density from observations of highredshift objects. Using the asymptotic solution, we investigate neutrino infallinto potential wells and show that it can be described on all scales by agrowth function that depends on time, wavenumber, and cosmological parameters.The growth function may be used to scale the present-day transfer functionsback in redshift. This allows us to construct the time-dependent transferfunction for each species from a single master function that is independent oftime, cosmological constant, and curvature.