Power-Law $f(R)$ Gravity Corrected Canonical Scalar Field Inflation

Abstract

The effective inflationary Lagrangian is a prominent challenge for theoretical cosmologists, since it may contain imprints of the quantum epoch. In view of the fact that higher order curvature terms might be present in the effective inflationary Lagrangian, in this work we introduce the theoretical framework of power-law $f(R)$ gravity corrected canonical scalar field inflation, aiming to study the inflationary dynamics of this new framework. The main characteristic of this new theoretical framework is the dominance of a power-law $f(R)$ gravity term $\sim R^n$, with $1<n<2$, compared to the Einstein-Hilbert term $\sim R$. In effect, the field equations are controlled by the $R^n$ term in contrast to the Einstein-Hilbert canonical scalar theory. We extract the slow-roll field equations and we calculate the slow-roll indices of the resulting theory which acquire quite elegant final form, when the slow-roll conditions hold true. Accordingly, we examine quantitatively the inflationary phenomenological implications of the theoretical framework we introduced, by choosing simple hybrid-like scalar field potentials. As we evince the resulting theory is in good agreement with the latest Planck data for a wide range of the free parameters of the model. Thus our theoretical framework makes possible to obtain viable inflationary theories, which otherwise would be non-viable, such as the simple power-law $f(R)$ gravity model or the simple power-law scalar model.