Thermal Damping of Neutrino-Coupled Scalar Dark Matter

TL;DR

Ultralight scalar dark matter that modulates neutrino masses can experience significant thermal damping from non-equilibrium cosmic neutrinos, yielding a damped equation of motion with a damping rate $\left<\Upsilon\right>_{\rm osc}$, a thermal mass $m_{\phi,\rm th}$, and a shifted minimum $\phi_{\rm th}$. The authors show that a high-temperature attractor $\Phi_\Upsilon(T)$ drives a thermal realignment mechanism in which a broad range of initial amplitudes converge to a predictable late-time abundance along a coupling-mass line $g\approx 1.8\times 10^{-11}\left(m_\phi/10^{-4}\ \mathrm{eV}\right)^{4/7}$, mitigating late-time constraints from BBN and CMB and opening experimental targets in the neutrino-scalar sector. This framework connects to MaVaN/NSI-type scenarios and suggests that other thermal dampers could yield similar attractor dynamics, potentially guiding future neutrino experiments and $0\nu\beta\beta$ searches toward the thermal-realignment target. The work thus provides a robust mechanism for realizing ultralight scalar DM with large initial misalignments while remaining consistent with cosmological bounds, and it highlights concrete phenomenological signatures and parameter-space targets for upcoming tests.

Abstract

We point out that ultralight scalar dark matter that modulates neutrino masses can be significantly thermal damped by cosmic neutrinos in the early universe. This dissipative effect arises as a backreaction from the neutrinos which are being driven slightly out of thermal equilibrium by the scalar. We estimate the rate of such thermal damping and explore its phenomenological implications. For a scalar that is produced early, we find that the effect of thermal damping results in a predictable final abundance largely insensitive to its initial condition while circumventing late time limits. This motivates a parameter-space line to target experimentally.

Figures (2)

• Figure 1: Evolution of the scalar amplitude $\Phi(T)$ as a function of (decreasing) temperature $T$. The thin solid lines are the $\Phi(T)$ for initial conditions such that $\Phi(T=50\mathinner{\mathrm{GeV}})=10^{17}\mathinner{\mathrm{GeV}},\ 10^{12}\mathinner{\mathrm{GeV}},\ 3\times 10^{10}\mathinner{\mathrm{GeV}}$, far above the finite-temperature minimum $\phi_{\rm th}$ (dotted line). The dashed lines are the $\Phi(T)$ for the same initial conditions, but with the thermal damping turned off, $\Upsilon=0$. On the $\vee$-shaped pink line labeled $\Phi_\Upsilon$, the oscillation-averaged thermal damping rate $\left<\Upsilon\right>_{\rm osc}$, c.f. Eq. \ref{['eq:Upsilonosc']}, is equal to Hubble dilution, $\left<\Upsilon\right>_{\rm osc}=2H$. This line stops at $T\approx 2\mathinner{\mathrm{MeV}}$, whereupon the neutrinos decouple. The gray prongs represent constraints from BBN (dark gray imposes three relativistic neutrinos, light gray imposes small $\Delta N_{\rm eff}$) and CMB (on the sum of neutrino masses). Here, the scalar-neutrino coupling $g$ and scalar mass $m_\phi$ are chosen such that the $\Phi$ at late times coincides with the amplitude corresponding to the measured DM density today, $\Phi_{\rm CDM}$ (blue band). Initial conditions of $\Phi$ that lie inside the basin of attractor shaded in light blue would track the left side of $\Phi_\Upsilon$, cross the thermal-damping attractor point ($\star$), c.f. Eq. \ref{['eq:Apoint']}, and converge onto the line that becomes $\Phi_{\rm CDM}$ at late times. The blue dot-dashed line marks the rough point from which the $\phi$ DM must behave as cold DM, with its amplitude scaling as $\Phi\propto a^{-3/2}$, in order to be consistent with large-scale structure observations. In particular, the transition from thermal-mass $m_{\phi,\rm th}$ dominated oscillation ($\Phi\propto a^{-1}$) to bare-mass $m_\phi$ dominated oscillation ($\Phi\propto a^{-3/2}$), marked with gray dashed line, must occur well before the blue dot-dashed line.
• Figure 2: The neutrino-scalar coupling $g$ vs scalar mass $m_\phi$ parameter space for cases with sufficiently large initial amplitudes $\Phi$ to be within the basin of attractor, c.f. Eq. \ref{['eq:basin']} and the light blue region of Fig. \ref{['fig:PhiT']}. On the blue line, the scalar hits the correct DM abundance at late times, c.f. \ref{['eq:target']}. The dashed part of the blue line is inconsistent with cosmic structure formation. The gray shaded regions are constraints from BBN and CMB. The BBN bound includes both the requirements of three relativistic neutrinos and small $\Delta N_{\rm eff}$. These limits are nearly identical and independent of $m_\phi$ if $\phi$ is thermal-mass dominated at $T=2\mathinner{\mathrm{MeV}}$, which occurs at $m_\phi\lesssim 10^{-11}\mathinner{\mathrm{eV}}$ along the BBN boundary. At higher $m_\phi$, the scalar becomes bare-mass dominated then, and its contribution to $\Delta N_{\rm eff}$ increases with $m_\phi$. It is a mere coincidence that the switching of the blue line from solid to dashed occurs at the boundary of the BBN limit. Also shown are the region ruled out by Super-K/SNO and the ultimate reach of KamLAND-Zen (KZ) $0\nu\beta\beta$ decay experiment as given in Ref. Huang:2021kam, assuming Eq. \ref{['eq:presentabundance']} and including a $3\times 10^{5}$ enhancement of the Galactic density relative to the cosmic average. We stop the plot at $m_\phi=0.1\mathinner{\mathrm{eV}}$ because beyond that point $\phi$ stops being wavelike in our Galaxy today.