Interactions of the scalaron dark matter in $f (R)$ gravity

In $f(R)$ gravity, the scalaron -- a scalar degree of freedom arising from modification of General Relativity -- could account for all dark matter in the universe if its mass lies in the meV--MeV range. In this work, we revisit the scalaron's interactions with Standard Model particles, assuming their minimal coupling to gravity. In particular, we provide a detailed calculation of the scalaron's decay rate into two photons -- a one-loop process of significant interest that has been the subject of discrepancies in the literature. We demonstrate that a direct evaluation of loop diagrams with appropriate regularisation eliminates the ambiguities inherent in methods relying on Jacobians from field redefinitions. Assuming the scalaron constitutes all of dark matter, we calculate the average cosmological background radiation produced by its decays into photons. We also estimate the contribution of primordial scalarons emitted in the hot early universe to the present dark matter density and find it to be negligible. Our results support all key aspects of the original scenario, in which scalaron dark matter behaves as a coherently oscillating field.