A Simple Analytic Treatment of Neutrino Mass Impact on the Full Power Spectrum Shape via a Two-Fluid Approximation

Understand

We present a new closed-form formula for the matter power spectrum in the presence of massive neutrinos that gives an accuracy of better than 5\% on all scales.

• It is the first closed-form result valid on all scales.
• To calculate this closed-form solution, we iteratively solve the fluid equations for cold dark matter+baryons, and neutrinos in terms of the neutrino mass fraction, $f_{\nu} \ll 1$, using variation of parameters to construct the response of the matter to the neutrino perturbation, which in turn will source the higher-order neutrino perturbations.
• This analytic solution accelerates calculations of the matter power spectrum with neutrinos.