What if ALP dark matter for the XENON1T excess is the inflaton

The recent XENON1T excess in the electron recoil data can be explained by anomaly-free axion-like particle (ALP) dark matter with mass mϕ = 2.3 ± 0.2 keV and the decay constant $$ {f}_{\phi }/{q}_e\simeq 2\times {10}^{10}\sqrt{\Omega_{\phi }/{\Omega}_{\mathrm{DM}}} $$ GeV. Intriguingly, the suggested mass and decay constant are consistent with the relation, $$ {f}_{\phi}\sim {10}^3\sqrt{m_{\phi }{M}_p} $$ , predicted in a scenario where the ALP plays the role of the inflaton. This raises a possibility that the ALP dark matter responsible for the XENON1T excess also drove inflation in the very early universe. We study implications of the XENON1T excess for the ALP inflation and thermal history of the universe after inflation. We find that the successful reheating requires the ALP couplings to heavy fermions in the standard model, which results in an instantaneous reheating and subsequent thermalization of the ALPs. Then, an entropy dilution of $$ \mathcal{O} $$ (10) is necessary to explain the XENON1T excess, which can be achieved by decays of the right-handed neutrinos.