Logarithmic corrected $F(R)$ gravity in the light of Planck 2015

TL;DR

This paper explores a modified $F(R)$ gravity model with a logarithmic correction, deriving solutions, scalar potentials, and stability conditions, and compares the model's cosmological parameters with Planck 2015 data.

Contribution

It introduces a new $F(R)$ gravity model with a logarithmic correction and analyzes its cosmological viability and stability properties.

Findings

Derived constant curvature solutions.

Found scalar potential and scalaron mass.

Identified stability conditions for the model.

Abstract

In this letter, we consider the theory of $F(R)$ gravity with the lagrangian density $ \pounds = R+\alpha R^2 + \beta R^2 \ln \beta R $. We obtain the constant curvature solutions and find the scalar potential of the gravitational field. We also obtain the mass squared of a scalaron in the Einstein$^,$s frame. We find cosmological parameters corresponding to the recent Plank 2015 results. Finally, we analyze the critical points and stability of the new modified theory of gravity and find that logarithmic correction is necessary to have successful model.