Randomness in the dark sector: Emergent mass spectra and Dynamical Dark Matter ensembles

In general, nonminimal models of the dark sector such as Dynamical Dark Matter posit the existence of an ensemble of individual dark components with differing masses, cosmological abundances, and couplings to the Standard Model. Perhaps the most critical among these features is the spectrum of masses, as this goes a long way towards determining the cosmological abundances and lifetimes of the corresponding states. Many different underlying theoretical structures can be imagined for the dark sector, each giving rise to its own mass spectrum and corresponding density of states. In this paper, by contrast, we investigate the spectrum of masses that emerges statistically from underlying processes which are essentially random. We find a density of states n(m) which decreases as a function of mass and actually has an upper limit m(max) beyond which n(m) = 0. We also demonstrate that this emergent density of states is particularly auspicious from the perspective of the Dynamical Dark Matter framework, leading to cosmological abundances and decay widths that are suitably balanced against each other across the dark-matter ensemble. Thus randomness in the dark sector coexists quite naturally with Dynamical Dark Matter, and we examine the prospects for observing the signals of such scenarios in dark-matter indirect-detection experiments.