Dark matter relic abundance from a critical-density instability

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.