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

TL;DR

This paper investigates the interactions of scalaron dark matter in $f(R)$ gravity, focusing on decay processes and cosmological implications, clarifying previous discrepancies and supporting the scalaron as a viable dark matter candidate.

Contribution

It provides a detailed, regularisation-based calculation of scalaron decay into photons, resolving previous ambiguities and confirming the scalaron's role as dark matter in $f(R)$ gravity.

Findings

Scalaron decay into photons is accurately calculated, resolving past discrepancies.

The cosmological background radiation from scalaron decay is quantified.

Primordial scalaron contribution to dark matter density is negligible.

Abstract

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.