Flows For The Masses: A multi-fluid non-linear perturbation theory for massive neutrinos

TL;DR

This paper introduces a fast, multi-fluid non-linear perturbation theory for massive neutrinos, improving accuracy over linear models and matching N-body simulations within 10% for relevant cosmological parameters.

Contribution

It extends the Time Renormalization Group perturbation theory to include massive neutrinos as non-linear fluids and accelerates computations using FFT techniques.

Findings

Achieves over two orders of magnitude speed-up in calculations.

Matches N-body simulations within 10% accuracy for certain neutrino fractions.

Reveals non-linear effects cause >10% correction to neutrino power spectrum at low densities.

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 $\Omega_{\nu,0} h^2 \leq 0.005$ 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 .