Neutrino Dark Energy -- Revisiting the Stability Issue

TL;DR

This work analyzes the stability of mass-varying neutrino (MaVaN) models by performing linear perturbation theory in a coupled scalar–neutrino system. By deriving a model-independent stability criterion that hinges on the scalar–neutrino coupling $eta$ and the ratio of neutrino to cold dark matter energy densities, the authors show that stability hinges on whether the scalar-mediated force is offset by CDM-driven gravitational drag. Through two representative potentials—the log-linear and inverse power-law models—they demonstrate that adiabatic MaVaN models can be stable up to the present if the coupling is moderate (with $ ho_ u$ subdominant to CDM), while strong couplings lead to negative adiabatic sound speed squared $c_a^2<0$ and rapid growth of neutrino perturbations, potentially forming neutrino nuggets. The results refine the previous no-go statements and indicate a viable parameter space for MaVaN dark energy, particularly for sub-eV neutrino masses, with implications for structure formation and future non-linear studies.

Abstract

A coupling between a light scalar field and neutrinos has been widely discussed as a mechanism for linking (time varying) neutrino masses and the present energy density and equation of state of dark energy. However, it has been pointed out that the viability of this scenario in the non-relativistic neutrino regime is threatened by the strong growth of hydrodynamic perturbations associated with a negative adiabatic sound speed squared. In this paper we revisit the stability issue in the framework of linear perturbation theory in a model independent way. The criterion for the stability of a model is translated into a constraint on the scalar-neutrino coupling, which depends on the ratio of the energy densities in neutrinos and cold dark matter. We illustrate our results by providing meaningful examples both for stable and unstable models.

Figures (8)

• Figure 1: The effective potential $V$ (thick lines), composed of the scalar potential $V_\phi$ (dashed) and the neutrino energy density $\rho_\nu$, plotted for three different redshifts, $z=5$ (solid), $z=4$ (dashed-dotted), $z=3$ (dotted). The VEV of $\phi$ tracks the minimum of $V$ (marked by X) and evolves to smaller values for decreasing redshift. We have used $\kappa=1\times10^{20} M_{\rm pl}^{-1}$ and $V_0=8.1\times10^{-13}$eV$^4$.
• Figure 2: The evolution of the effective coupling, $\beta$ (given by Eq. (\ref{['eq:betalln']})), as a function of redshift for the potential Eq. (\ref{['eq:lln']}). We have used $\kappa=1\times 10^{20} M_{\rm pl}^{-1}$ and $V_0=8.1\times10^{-13}$eV$^4$.
• Figure 3: The effective potential $V$ (thick lines), composed of the scalar potential $V_\phi$ (dotted) and the neutrino energy density $\rho_\nu$, plotted for two different redshifts, $z=1$ (dot-dashed), $z=0$ (dashed). The VEV of $\phi$ tracks the minimum of $V$ (marked by X) and evolves to larger values for decreasing redshift. We have used $n=0.01$ and $M=0.011$ eV.
• Figure 4: The evolution of the effective coupling, $\beta$ (given by Eq. (\ref{['eq:betapow']})), as a function of redshift for the potential Eq. (\ref{['eq:pow']}). We have used $\sigma=100 M_{\rm pl}^{-2}$.
• Figure 5: $a)$ Neutrino mass $m_\nu$ (solid) and temperature $T_\nu$ (dotted) as a function of redshift. $b)$ Total dark energy sound speed squared $c^2_a$ as a function of redshift. $c)$ Density contrast in neutrinos (oscillating) $\delta_\nu$ and density contrast in CDM $\delta_{\rm CDM}$ as a function of redshift on a scale $k=0.1\,{\rm Mpc}^{-1}$. We have used $\kappa=1\times10^{20} M_{\rm pl}^{-1}$ and $V_0=8.1\times10^{-13}$eV$^4$.