📝 SummarXiv

Abstract

One of the key features of the $R^2$-gravity is the embedding of a scalar field, scalaron, into the gravity sector. The scalaron interacts with the Standard Model (SM) matter fields through Planck-suppressed couplings. If the scalaron serves as a viable dark matter (DM) candidate, it can account for the lack of evidence of DM interactions beyond gravity in experimental and observational probes to date. The realization of the scalaron, as a cold DM candidate, depends on an induced trilinear interaction with the SM Higgs, despite its suppressed coupling strength. Here, we introduce a Higgs non-minimal coupling to gravity that additionally contributes to the induced trilinear interaction with its existing competing part, originated from the $R^2$-gravity. We study the interplay between these two contributions in the early universe, which determines both the initial conditions and evolution of the scalaron, leading to cold DM behavior at a later epoch. The trilinear interaction vanish identically for certain combinations of the Higgs non-minimal coupling and the scalaron mass, thereby setting the scalaron density through misalignment mechanism, similar to axions. Consequently, we find that the observed DM relic density is obtained for a scalaron mass between $1.38$ keV and $0.7$ MeV. The lower limit on the mass stems from the LHC constraints on the Higgs non-minimal coupling, whereas the upper bound arises from INTEGRAL/SPI limits on the excess gamma-ray flux from possible scalaron decays to two photons.