The Effect of Thermal Neutrino Motion on the Non-linear Cosmological Matter Power Spectrum

TL;DR

This study addresses how thermal neutrino motion affects non-linear structure formation and the matter power spectrum by performing N-body simulations that explicitly include neutrino thermal velocities in a two-species cosmology. It finds that non-linear evolution enhances the suppression relative to linear theory, with a maximum around $\Delta P/P|_{\max} \sim -9.8\,\Omega_\nu/\Omega_m$ at $k \sim 0.5-1\,h\,\mathrm{Mpc}^{-1}$, and reveals a turnover due to mode coupling. The authors derive a simple analytic expression for neutrino-induced suppression and introduce a fast method to incorporate massive neutrinos in simulations at the 1% level for $\sum m_\nu \lesssim 0.15$ eV. These results are essential for interpreting upcoming high-precision surveys and for robustly constraining neutrino masses from cosmological data.

Abstract

We have performed detailed studies of non-linear structure formation in cosmological models with light neutrinos. For the first time the effect of neutrino thermal velocities has been included in a consistent way, and the effect on the matter power spectrum is found to be significant. The effect is large enough to be measured in future, high precision surveys. Additionally, we provide a simple but accurate analytic expression for the suppression of fluctuation power due to massive neutrinos. Finally, we describe a simple and fast method for including the effect of massive neutrinos in large-scale N-body simulations which is accurate at the 1% level for \sum m_nu < 0.15 eV.

Figures (7)

• Figure 1: The linear theory transfer functions at $z=4$ for the CDM and neutrino components.
• Figure 2: Images of the CDM and neutrino density distributions in a slice of the simulation volume. The images span $512\,h^{-1} \, {\rm Mpc}$ on a side and has a depth of $10\,h^{-1}\, {\rm Mpc}$. To produce the images we have interpolated the masses of the N-body particles to a regular grid with the adaptive smoothing kernel of monaghan. The images show the densities for the CDM component (left), neutrinos with $\sum m_\nu=0.6 \, {\rm eV}$ (middle), and neutrinos with $\sum m_\nu=0.3 \, {\rm eV}$ (right). The top row is at $z_i=4$ and the bottom row at $z=0$. To enhance the dynamic range of the CDM structures the square root has been taken of the CDM density field in the $z=0$ image. The $\sum m_\nu=0.3 \, {\rm eV}$ neutrino image at $z=0$ displays artificial small-scale structures in the voids caused by neutrino $N$-body particle shot-noise. All the images are made from simulations with $512^3$ neutrino $N$-body particles.
• Figure 3: The cumulative Fermi-Dirac distributions as a function of velocity for most of the simulations listed in Table \ref{['fig:table1']}.
• Figure 4: Relative differences in the matter power spectra at $z=0$ between pure $\Lambda$CDM models and models with neutrinos included. The differences expected from linear theory are also shown. The horizontal black lines indicate a relative power spectrum suppression of $-9.8 \, \Omega_\nu / \Omega_m$.
• Figure 5: Top left: Differences in $\%$ in the matter power spectra at $z=0$ with $\sum m_\nu=0.6$ eV neutrinos and $z_i=4$. The differences are taken with respect to the $1024^3$ neutrino simulation. Top right: Neutrino power spectra at $z=0$ with $\sum m_\nu=0.6$ eV neutrinos and $z_i=4$. Bottom left: Differences in $\%$ in the matter power spectra at $z=0$ with $\sum m_\nu=0.3$ eV neutrinos and $z_i=4$. The differences are taken with respect to the $512^3$ neutrino simulation. Bottom right: Neutrino power spectra at $z=0$ with $\sum m_\nu=0.3$ eV neutrinos and $z_i=4$.