On Inflation and Axionic Dark Matter in a Scaled Gravity

Abstract

Motivated by the modified gravity theories $F(R)\neq R$ and inflationary physics, we first propose and investigate an inflation model in a scaled gravity $F(R)=R\,+βR$, where $β$ is a dimensionless scaling parameter. The latter is also implemented in a particular potential $V(ϕ)=M^{4}\left[ 1-\cos \left( \frac{ϕ}μ\right)^{β}\right] $ being considered to drive the inflation via a parameter coupling scenario. Using the slow-roll approximations, the gravity scale parameter $β$ is approached with respect to the range of the associated computed cosmological observables $n_{s}$ and $r$ according to the recent Planck and BICEP/Keck data. Then, we discuss the axionic dark matter in the suggested gravity model by considering the case where the inflaton is taken to be identified with an axion-like field $ϕ=f_{a}θ$ with the decay constant $f_{a}=μ$. Referring to the known data, the underlying inflation scale $M$ is constrained to be much lower than the corresponding axion scale $M\ll f_{a}$.