Unimodular $F(R)$ Gravity

TL;DR

This paper develops a modified unimodular $F(R)$ gravity framework, enabling the realization of diverse cosmological scenarios, including inflationary models compatible with observational data, by extending the formalism and equations of motion.

Contribution

It introduces a novel formalism for unimodular $F(R)$ gravity that allows for new cosmological solutions not possible in standard unimodular gravity.

Findings

Several inflationary scenarios compatible with Planck and BICEP2 data.

Extended formalism enables realization of diverse cosmological models.

Derived equations of motion for unimodular $F(R)$ gravity.

Abstract

We extend the formalism of the Einstein-Hilbert unimodular gravity in the context of modified $F(R)$ gravity. After appropriately modifying the Friedmann-Robertson-Walker metric in a way that it becomes compatible to the unimodular condition of having a constant metric determinant, we derive the equations of motion of the unimodular $F(R)$ gravity by using the metric formalism of modified gravity with Lagrange multiplier constraint. The resulting equations are studied in frames of reconstruction method, which enables us to realize various cosmological scenarios, which was impossible to realize in the standard Einstein-Hilbert unimodular gravity. Several unimodular $F(R)$ inflationary scenarios are presented, and in some cases, concordance with Planck and BICEP2 observational data can be achieved.