Slow neutrinos: non-linearity and momentum-space emulation

TL;DR

The paper develops a fast linear-response solver for non-relativistic neutrinos, FAST-nu f, enabling millisecond-scale calculations of neutrino clustering and momentum-space structure. Building on this, it constructs Cosmic-E$\nu$-II, a momentum-space emulator that divides the non-linear neutrino problem into a fast linear response and a non-linear enhancement ratio $\mathcal{R}(a,k,u)$, dramatically improving small-scale and low-$M_\nu$ accuracy and extending to normal and inverted mass orderings. The approach reduces training data dynamic range and increases momentum resolution, achieving sub-10% predictions for neutrino densities in halo outskirts ($2R_{\rm v} \lesssim r \lesssim 10R_{\rm v}$) and enabling practical cross-checks on neutrino mass and ordering. The work also demonstrates a halo-painting technique to predict neutrino density profiles around massive halos, validating the method against N-body simulations and highlighting IO-DO differences in clustering behavior.

Abstract

Recent cosmological bounds on the sum of neutrino masses, M_nu = sum m_nu, are in tension with laboratory oscillation experiments, making cosmological tests of neutrino free-streaming imperative. In order to study the scale-dependent clustering of massive neutrinos, we develop a fast linear response method, FAST-nu f, applicable to neutrinos and other non-relativistic hot dark matter. Using it as an accurate linear approximation to help us reduce the dynamic range of emulator training data, based upon a non-linear perturbation theory for massive neutrinos, we improve the emulator's accuracy at small M_nu and length scales by a factor of two. We significantly sharpen its momentum resolution for the slowest neutrinos, which, despite their small mass fraction, dominate small-scale clustering. Furthermore, we extend the emulator from the degenerate to the normal and inverted mass orderings. Applying this new emulator, Cosmic-Enu-II, to large halos in N-body simulations, we show that non-linear perturbation theory can reproduce the neutrino density profile in the halo outskirts, 2R_vir < r < 10R_vir , to better than 10%.

Figures (19)

• Figure 1: Accuracy of fast-$\nu f$ for the total neutrino density contrast $\delta_\nu(a,k)$. Shown is the fractional difference between fast-$\nu f$ and class computations. Dashed lines denote negative values, $\delta_\nu^{({\rm FAST}\nu f)} < \delta_\nu^{\rm (CLASS)}$. The two agree to better than $1\%$ for all $a \geq 0.2$ and $0.003 \leq k[h/{\rm Mpc}] \leq 15$.
• Figure 2: Accuracy of fast-$\nu f$ for individual neutrino flows with a non-linear $\delta_{\rm cb}$ source. fast-$\nu f$ flows (lines) closely match flows computed using the MuFLR linear response code of Chen:2020bdf (points), for a $\nu\Lambda$CDM model with $M_\nu=150$ meV (NO) at $z=0$. fast-$\nu f$ is as accurate as MuFLR but much faster, allowing us to compute $\delta(a,k,u)$ for many flows.
• Figure 3: Broad features of the non-linear enhancement ratio ${\mathcal{R}}(a,k,u)$ of Eq. (\ref{['e:Rnu_a_k_u']}) at $a=1$, for the E600DO model of Table \ref{['t:nLCDM_models']}. For $k\leq 1~h/$Mpc, it has a low dynamic range, making interpolation accurate. The inset shows the high-$u$ region in greater detail, confirming that ${\mathcal{R}}<1$ at high $u$.
• Figure 4: Breakdown of the FlowsForTheMasses closure approximation of Chen:2022cgw, which assumes that neutrino non-linearity is small below $k=k_{\rm fs}(a,u)$ (identified by vertical arrows). ${\mathcal{R}}(a,k,u)$ for the E600DO model of Table \ref{['t:nLCDM_models']} (solid lines), precisely corresponding to that of Fig. \ref{['f:Rc_wide']}, disagrees with the $u=0$ Time-RG points (triangles along the vertical axis). An alternative closure approximation (dashed lines; see text) improves agreement with Time-RG at low $u$ without modifying ${\mathcal{R}}$ to the right of the arrows, showing this region to be insensitive to our chosen approximation. This motivates a simple interpolation between the Time-RG point and the $k \geq k_{\rm fs}(a,u)$ region in order to avoid underpredicting ${\mathcal{R}}$. For reference, the region to the left of the vertical dotted line represents $1\%$ of the neutrino number density.
• Figure 5: Interpolation and extrapolation of the non-linear enhancement ratio ${\mathcal{R}}(a,k,u)$ for the E600DO model of Table \ref{['t:nLCDM_models']}. At low $u$, interpolation (dotted lines) between the Time-RG values (large triangular points) and the Cosmic-E$\nu$ training data (small square points) avoids the underpredictions of ${\mathcal{R}}$ evident in the solid and dashed lines, corresponding to the two closure approximations of Fig. \ref{['f:Rc_slow']}. The training data approximately cover the free-streaming region $k \geq k_{\rm fs}(a,u)$, to the right of the vertical arrows. Meanwhile, at high $u$, extrapolation (dotted lines) using the training data matches direct calculation of ${\mathcal{R}}$ (solid lines) to a few percent.