The Inflaton Portal to a Highly decoupled EeV Dark Matter Particle

We explore the possibility that the dark-matter relic abundance is generated in a context where the inflaton is the only mediator between the visible and the hidden sectors of our universe. Due to the relatively large mass of the inflaton field, such a portal leads to an extremely feeble interaction between the dark and the visible sectors suggesting that the dark sector cannot reach any thermal equilibrium with the visible sector. After the two sectors are populated by the decay of the inflaton, a heavy dark-matter particle thermally decouples within the dark sector. Later, a lighter dark particle, whose decay width is naturally suppressed by the inflaton propagator, decays into the visible sector after it dominates the energy density of universe. This process dilutes the dark-matter relic density by injecting entropy in the visible sector. We show that an inflaton mass of $\mathcal{O}(10^{13})$ GeV together with couplings of order one are fully compatible with a dark-matter relic abundance $\Omega h^2\sim 0.1$. As a general feature of the model, the entropy dilution mechanism is accompanied by a period of early matter domination, which modifies the amount of e-folds of inflation necessary to accommodate Planck data. Moreover, the coupling of the inflaton to the dark and visible sectors brings loop contributions to the inflationary potential which can destabilize the inflation trajectory. Considering all these complementary constraints, we show that, in the context of a plateau-inflation scenario such as the $\alpha$-attractor model, the inflaton can constitute a viable mediator between the visible sector and a $\sim 10$ EeV dark-matter candidate. Furthermore, we show that improved constraints on the tensor-to-scalar ratio and spectral index could potentially rule out dark-matter scenarios of this sort in the future.