Abstract
We investigate the physics of dark matter models featuring composite bound states carrying a large conserved dark "nucleon" number. The properties of sufficiently large dark nuclei may obey simple scaling laws, and we find that this scaling can determine the number distribution of nuclei resulting from Big Bang Dark Nucleosynthesis. For plausible models of asymmetric dark matter, dark nuclei of large nucleon number, e.g. > 10^8, may be synthesised, with the number distribution taking one of two characteristic forms. If small-nucleon-number fusions are sufficiently fast, the distribution of dark nuclei takes on a logarithmically-peaked, universal form, independent of many details of the initial conditions and small-number interactions. In the case of a substantial bottleneck to nucleosynthesis for small dark nuclei, we find the surprising result that even larger nuclei, with size >> 10^8, are often finally synthesised, again with a simple number distribution. We briefly discuss the constraints arising from the novel dark sector energetics, and the extended set of (often parametrically light) dark sector states that can occur in complete models of nuclear dark matter. The physics of the coherent enhancement of direct detection signals, the nature of the accompanying dark-sector form factors, and the possible modifications to astrophysical processes are discussed in detail in a companion paper.
Highlights
Standard Model (SM) nuclei, there is a relatively short-range strong “nuclear” binding force with a hard core repulsion, and there is an approximately-conserved quantum number, DNN, analogous to baryon number
The properties of sufficiently large dark nuclei may obey simple scaling laws, and we find that this scaling can determine the number distribution of nuclei resulting from Big Bang Dark Nucleosynthesis
In this paper we have studied the “Big Bang dark nucleosynthesis” process by which ‘nuclear’ bound states of DM may be built up in the early universe
Summary
While present-day DM may be composed of large bound states, this is generically not the case in the hot early universe. At large temperatures T , the entropy term in the free energy dominates and the chemical equilibrium distribution has almost all DM in small-number states. For small T , compared to the binding energies, the energy term dominates, and chemical equilibrium favours large bound states. For the DM masses we consider, the DM is dilute, if we are in kinetic equilibrium the transition from being kept in equilibrium by dissociations, to fusion reactions dominating, generally happens fast enough to be only a small perturbation to the subsequent fusion process (this technical point is discussed in detail in appendix A). If thermalising interactions are not sufficiently fast to reduce the energy of de-excitation products before they hit another DN, these may cause dissociations, leading to very different behaviour from the fusions-only approximation (cf SM recombination).. Regime in the current paper, assuming instead that the de-excitation products decay or thermalise on fast enough timescales.
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