Dark matter relic abundance from a critical-density instability

Abstract

We study a nonstandard dark-matter thermal history in which strong self-interactions give rise to collective many-body effects at high number density, as in strongly interacting quantum media. At early times, dark matter occupies a correlated phase in which its coupling to a light mediator is dynamically screened, suppressing annihilation far below the perturbative rate. As the Universe expands and the number density decreases, this screened phase becomes unstable at a critical density n_c, triggering a rapid, far-from-equilibrium annihilation episode. We show that this annihilation burst fixes the final relic abundance, which is governed primarily by n_c rather than by the microscopic annihilation coupling. Using a minimal effective parametrization, we solve the resulting modified Boltzmann evolution and map the viable parameter space. For TeV-scale dark matter and sub-GeV mediators, we find relic abundances consistent with observations together with self-interaction cross sections relevant for small-scale structure, realizing a consistent and predictive nonstandard thermal history.

Figures (6)

• Figure 1: Density-dependent effective annihilation rate $\langle\sigma v\rangle_{\rm eff}/\langle\sigma v\rangle_0$ as a function of the DM number density $n_\chi$. Cosmological dilution corresponds to right-to-left evolution along the horizontal axis. At $n_\chi\simeq n_c$ the screened phase becomes unstable, the interaction effectively unscreens, and an annihilation burst is triggered.
• Figure 2: Screen--burst--freeze relic-density map in the $(m_\chi,m_\phi)$ plane. Colors show the predicted abundance normalized to the observed value, $\log_{10}(\Omega_\chi/\Omega_{\rm DM})$, obtained from the modified Boltzmann evolution with a density-dependent screened phase followed by an instability-driven unscreening (annihilation "burst").The solid black contour satisfies $\Omega_\chi h^2=\Omega_{\rm DM}h^2$. The hatched region indicates an estimated loss of perturbative control (partial-wave unitarity/perturbativity criterion; see Sec. \ref{['sec:unitarity']}), where the microscopic $2\to2$ treatment entering $\langle\sigma v\rangle_0$ may no longer be reliable. The parameter box lists the benchmark SBF history parameters used for the scan: $(T_c,\alpha,\Gamma_{\rm inst}/H,\Delta\log_{10}x,\delta\log_{10}x)$.
• Figure 3: Phase diagram of the screen--burst--freeze mechanism in the $(\alpha,\,y_\chi)$ plane. Colors indicate the relic abundance normalized to the observed value, $\Omega_\chi/\Omega_{\rm obs}$. The solid black contour corresponds to solutions reproducing the observed dark-matter abundance, while the dashed curve shows the standard thermal freeze-out prediction obtained with a constant perturbative annihilation rate. At sufficiently large screening strength $\alpha$, a horizontal attractor band emerges in which the relic abundance is determined primarily by the instability density $n_c$ and becomes insensitive to the microscopic coupling $y_\chi$.
• Figure 4: Evolution of the comoving yield $Y(x)$ for a benchmark realizing the screen--burst--freeze mechanism (green), compared with standard thermal freeze-out using the same perturbative cross section (orange). The annihilation burst at $n_\chi\simeq n_c$ sharply reduces the yield, fixing the relic abundance.
• Figure 5: Screen--Burst--Freeze viability and coupling attractor. Left: Viable parameter space in the $(T_c,\Gamma_{\rm inst}/H)$ plane for a representative benchmark. Shaded regions indicate exclusion by neutrino decoupling ($T_c<5~\mathrm{MeV}$) and by the requirement of a sudden instability-driven burst ($\Gamma_{\rm inst}/H<10$). The thick curve denotes the boundary reproducing the observed relic abundance, while thin curves are iso-contours of the microscopic coupling $y_{\rm req}$. The near-horizontal iso-$y_{\rm req}$ structure demonstrates that once the instability is triggered, the relic abundance is controlled primarily by the critical density $n_c$ (or equivalently $T_c$), with only weak dependence on the annihilation coupling. Right: Probability density of $\log_{10} y_{\rm req}$ over the viable region, showing a narrow attractor band that quantifies the coupling insensitivity characteristic of the screen--burst--freeze mechanism.