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

Velocity dispersion of the massive neutrinos presents a daunting challenge for nonlinear 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 Q & nu;,0h2 G 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 St & nu;,0h2 = 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.

Automated summary

The velocity dispersion of massive neutrinos is a challenging problem for nonlinear cosmological perturbation theory. In this study, we treat the neutrino population as a collection of nonlinear fluids with uniform initial momentum using an extension of the Time Renormalization Group perturbation theory. By using recently-developed Fast Fourier Transform techniques, we significantly accelerate the nonlinear perturbation theory, achieving a speed that is practical for use. Our results show good agreement with N-body neutrino simulations up to a 10% error level, demonstrating the limitations of linear theory in predicting the neutrino power spectrum accurately. The non-linear growth correction to the neutrino power spectrum can be significant even for low density fractions, highlighting the importance of considering non-linear effects.