  Velocity dispersion of the massive neutrinos presents a daunting challenge
for non-linear cosmological perturbation theory. We consider the neutrino
population as a collection of non-linear fluids, each with uniform initial
momentum, through an extension of the Time Renormalization Group perturbation
theory. Employing recently-developed Fast Fourier Transform techniques, we
accelerate our non-linear perturbation theory by more than two orders of
magnitude, making it quick enough for practical use. After verifying that the
neutrino mode-coupling integrals and power spectra converge, we show that our
perturbation theory agrees with N-body neutrino simulations to within 10% for
neutrino fractions $\Omega_{\nu,0} h^2 \leq 0.005$ up to wave numbers of k = 1
h/Mpc, an accuracy consistent with 2.5% errors in the neutrino mass
determination. Non-linear growth represents a >10% correction to the neutrino
power spectrum even for density fractions as low as $\Omega_{\nu,0} h^2 =
0.001$, demonstrating the limits of linear theory for accurate neutrino power
spectrum predictions. Our code FlowsForTheMasses is avaliable online at
github.com/upadhye/FlowsForTheMasses .
