Oleg Lebedev and colleagues studied scalar dark matter production and reheating via direct inflaton/renormalizable couplings. They found that dark matter (DM) can be abundantly produced even at very small couplings. Their study recently appeared in Arxiv.
The unique renormalizable gauge–invariant interaction between the Standard Model and the inflaton φ has the form:
It is thus natural to expect that these couplings play a leading role in producing the Standard Model (SM) particles after inflation, i.e. reheating. If dark matter is a scalar field s, analogous renormalizable terms can be written down for the interaction between inflation and scalar field. Although a similar statement applies to the Higgs–DM interaction, in the present work Lebedev and colleagues focused on non–thermal dark matter and assumed that such couplings are negligible. The above interactions are sufficient to fully describe both dark matter production and reheating.
After inflation ends, the inflaton oscillation epoch sets in. During this epoch, particle production can be very efficient. Indeed, renormalizable couplings of the above type can lead to parametric or tachyonic resonance signifying explosive particle production. However, Lebedev and colleagues by using LATTICEEASY tool, found that the collective effects such as resonances, back scattering and rescattering of the produced particles make a crucial impact on the dynamics of the system and the resulting dark matter abundance. In particular, the produced DM quanta can efficiently scatter against the inflaton background thereby destroying it and possibly bringing the system to quasi–equilibrium state. In this case, the dark matter abundance becomes independent of the inflaton–dark matter coupling and is described by a universal formula.
“The renormalizable inflaton couplings to dark matter and the Higgs field are sufficient to fully describe the reheating and DM production, leading to a realistic picture of the Early Universe.”, they concluded.
Reference: Oleg Lebedev, Fedor Smirnov, Timofey Solomko, Jong-Hyun Yoon, “Dark matter production and reheating via direct inflaton couplings: collective effects”, pp. 1-19, 2021.
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