On Inflation and Axionic Dark Matter in a Scaled Gravity

Abstract

Motivated by the modified gravity theories $F(R)\ne R$ and inflationary physics, we first propose and investigate an inflation model in a scaled gravity $F(R)=R+\beta R$, where $\beta$ is a dimensionless scaling parameter. The latter is also implemented in a particular potential $V(\varphi )=M^4\left[1-\cos {\left(\frac{\varphi }{\mu }\right)}^{\beta }\right]$ being considered to drive the inflation via a parameter coupling scenario. Using the slow-roll approximations, the gravity scale parameter $\beta$ 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 $\varphi =f_a\theta$ with the decay constant $f_a=\mu$. Referring to the known data, the underlying inflation scale $M$ is constrained to be much lower than the corresponding axion scale $M\ll f_a$.

Latex, 18pages, 2figures, Authors in Alphabetical order