Flows for the masses: A multi-fluid non-linear perturbation theory for massive neutrinos

Abstract

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 Ω ν,0 h 2 ≤ 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 Ω ν,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.