Ghost-free non-local $F(R)$ Gravity Cosmology

TL;DR

This paper develops ghost-free non-local $F(R)$ gravity models, explores their cosmological solutions, stability, and inflationary phenomenology, demonstrating viability with observations especially for power-law models under constant-roll conditions.

Contribution

It introduces a method to eliminate ghosts in non-local $F(R)$ gravity and analyzes their cosmological and inflationary implications, highlighting model-dependent results.

Findings

Ghost degrees of freedom can be removed in non-local $F(R)$ gravity.

Power-law models with $1<n<2$ can produce viable inflation.

The $R^2$ model's inflationary viability depends on specific conditions.

Abstract

In this work we shall study ghost-free non-local $F(R)$ gravity models. Firstly we shall demonstrate how the ghost degrees of freedom may occur in the non-local $F(R)$ gravity models, and accordingly we shall modify appropriately the gravitational action of non-local $F(R)$ gravity models in order to eliminate the ghosts. Also we shall investigate how the (anti-)de Sitter and the Minkowski spacetime cosmological solutions may arise in the theory, and we investigate when these solutions are stable. Moreover, we shall examine the inflationary phenomenology of the Jordan frame ghost-free non-local $F(R)$ gravity. We shall study two $F(R)$ gravity models, the power law $F(R)$ gravity model $\sim R^n$ with $1<n<2$, $n\neq 2$ and the $R^2$ model, assuming that the slow-roll condition holds true for the Hubble rate during the inflationary era $\dot{H}\ll H^2$ and that the general constant-roll condition $\ddot{\phi}=3\beta H\dot{\phi}$ holds true for the evolution of the scalar field, which includes the slow-roll case for $\beta=0$. As we shall demonstrate, the power-law non-local $F(R)$ gravity case can produce a viable inflationary era, compatible with observations, in the constant-roll case, unlike for the $R^2$ model. It is conceivable that the results are model dependent, as in the ordinary vacuum $F(R)$ gravity.