Massive Neutrinos and the Non-linear Matter Power Spectrum

TL;DR

The paper tackles how massive neutrinos modify the non-linear matter power spectrum and develops an accurate HALOFIT-ν fitting formula calibrated to high-resolution N-body simulations with $M_ u$ in [0.15,0.6] eV. It shows that standard HALOFIT over-predicts non-linear suppression due to neutrino free-streaming because it neglects back-reaction from non-linear dark matter growth, and it provides a calibrated model that better reproduces the redshift- and scale-dependent features of the suppression. The improved model uses targeted modifications to HALOFIT’s quasilinear and nonlinear terms and adds a back-reaction term with coefficients fit to simulations, achieving about 2% accuracy for $z\le3$ and $k<7 h Mpc^{-1}$, with CAMB patches for practical use. The results enhance the reliability of neutrino-mass forecasts for upcoming galaxy, Lyman-α forest, and weak-lensing surveys, while recognizing limitations at higher redshift ($z>3$) and for diverse cosmologies, where hydro simulations may still be required.

Abstract

We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k ~ 1 hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced neutrino suppression over the targeted scales and redshifts significantly better. We test its robustness with regard to changing cosmological parameters and a variety of modelling effects.

Figures (6)

• Figure 1: Matter power spectra from a simulation with massive neutrinos (dashed lines), and $M_\nu = 0.6$ eV, compared to the corresponding power spectra from a $\Lambda$CDM simulation (solid lines). Dotted lines show the linear theory prediction for massive neutrinos, while dot-dashed lines show the linear theory prediction for $\Lambda$CDM. Upper (green) lines show spectra at $z=0$, while lower (black) lines show them at $z=1$. The simulations shown are S60 (small scales) and L60 (large scales), whose parameters are described in Table \ref{['tab:partsimuls']}. S60 shows only modes where $k > 4 \times 2\pi /$ Box-size, so sample variance is small, and L60 is cut off at $k= 0.4 \,h \mathrm{Mpc}^{-1}$, for clarity. Note that the absolute power spectrum is slightly less converged with respect to box size than the ratio of the massive neutrino power spectrum with and without massive neutrinos.
• Figure 2: The ratio between the matter power spectrum at $z=0$ (Left) and $z=1$ (Right) for simulations with and without massive neutrinos ($M_\nu = 0.6$ eV). Solid green lines show results for simulations using particles, while dashed red lines show results from Fourier-space simulations. The black dot-dashed lines show the predicted effect from linear theory. The simulations used were L60 and S60; box sizes were $512\,\mathrm{Mpc} \,h^{-1}$ and $150\,\mathrm{Mpc} \,h^{-1}$, with parameters shown in Table \ref{['tab:partsimuls']}. For the smaller box sizes, more than one realisation of structure is available, and hence we show (dotted grey lines) the one $\sigma$ error due to sample variance, as estimated numerically. Particle and Fourier-space methods use the same initial structure realisations. The Fourier-space method has more power in the largest scale mode, probably because the phase structure of the neutrino component has been prevented from evolving, enhancing the effect of sample variance.
• Figure 3: The effect of massive neutrinos on the matter power spectrum for a neutrino mass of $M_\nu = 0.6$ eV. Solid lines show the ratio between simulations with and without massive neutrinos, for both L60 (red), with a $512\,\mathrm{Mpc} \,h^{-1}$ box and S60 (orange), with a $150\,\mathrm{Mpc} \,h^{-1}$ box. Initial redshift was $99$. The blue dashed line shows the estimated ratio using HALOFIT , while the black dashed line shows the prediction from linear theory.
• Figure 4: The effect of massive neutrinos on the matter power spectrum for a neutrino mass of $M_\nu = 0.3$ eV. Solid lines show the ratio between simulations with and without massive neutrinos, for both L30 (red), with a $512\,\mathrm{Mpc} \,h^{-1}$ box and S30 (orange), with a $150\,\mathrm{Mpc} \,h^{-1}$ box. Initial redshift was $49$. The blue dashed line shows the estimated ratio using HALOFIT , while the black dashed line shows the prediction from linear theory.
• Figure 5: The effect of massive neutrinos on the matter power spectrum for a neutrino mass of $M_\nu = 0.15$ eV. Solid lines show the ratio between simulations with and without massive neutrinos, for both L15 (red), with a $512\,\mathrm{Mpc} \,h^{-1}$ box and S15 (orange), with a $150\,\mathrm{Mpc} \,h^{-1}$ box. Initial redshift was $24$. The blue dashed line shows the estimated ratio using HALOFIT , while the black dashed line shows the prediction from linear theory.