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Cosmology is poised to measure the neutrino mass sum M ν and has identified several smaller-scale observables sensitive to neutrinos, necessitating accurate predictions of neutrino clustering over a wide range of length scales. The FlowsForTheMasses non-linear perturbation theory for the the massive neutrino power spectrum, |$\Delta ^2_\nu (k)$|⁠ , agrees with its companion N -body simulation at the |$10~{{\ \rm per\ cent}}-15~{{\ \rm per\ cent}}$| level for k ≤ 1  h  Mpc−1. Building upon the Mira-Titan IV emulator for the cold matter, we use FlowsForTheMasses to construct an emulator for |$\Delta ^2_\nu (k)$|⁠ , Cosmic-Eν , which covers a large range of cosmological parameters and neutrino fractions Ων, 0 h 2 ≤ 0.01 (M ν ≤ 0.93 eV). Consistent with FlowsForTheMasses at the 3.5 per cent level, it returns a power spectrum in milliseconds. Ranking the neutrinos by initial momenta, we also emulate the power spectra of momentum deciles, providing information about their perturbed distribution function. Comparing a M ν = 0.15 eV model to a wide range of N -body simulation methods, we find agreement to 3 per cent for k ≤ 3 k FS = 0.17  h  Mpc−1 and to 19 per cent for k ≤ 0.4  h  Mpc−1. We find that the enhancement factor, the ratio of |$\Delta ^2_\nu (k)$| to its linear-response equivalent, is most strongly correlated with Ων, 0 h 2, and also with the clustering amplitude σ8. Furthermore, non-linearities enhance the free-streaming-limit scaling |$\partial \log (\Delta ^2_\nu /\Delta ^2_{\rm m}) / \partial \log (M_\nu)$| beyond its linear value of 4, increasing the M ν-sensitivity of the small-scale neutrino density. [ABSTRACT FROM AUTHOR]

Modern cosmological surveys are delivering data sets characterized by unprecedented quality and statistical completeness; this trend is expected to continue in the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the non-linear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. We have recently introduced the Mira–Titan Universe simulation suite designed to construct emulators for a range of cosmological probes. This gravity-only set of simulations covers the standard six cosmological parameters {ωm, ωb, σ8, h ,  n s, w 0} and, in addition, includes massive neutrinos and a dynamical dark energy equation of state {ων, w a}. In this paper, we present the final emulator for the matter power spectrum based on 111 cosmological simulations, each covering a (2.1 Gpc)3 volume and evolving 32003 particles. An additional set of 1776 lower resolution simulations and TimeRG perturbation theory results for the power spectrum are used to cover scales straddling the linear to mildly non-linear regimes (maximum wavenumber k  = 5 Mpc−1). The emulator provides predictions at the 2–3 per cent level of accuracy over a wide range of cosmological parameters and is publicly released as part of this paper. [ABSTRACT FROM AUTHOR]