Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint

TL;DR

This paper introduces two novel ghost-free $F(R)$ gravity models with Lagrange multiplier constraints, unifying mimetic and Jordan frame descriptions, capable of realizing various cosmological scenarios including de Sitter solutions.

Contribution

The paper develops two new ghost-free $F(R)$ gravity models with Lagrange multipliers, connecting mimetic and Jordan frame formulations, and demonstrating their cosmological applications.

Findings

Existence of de Sitter solutions in the models

Unification of mimetic and Jordan frame $F(R)$ gravity

Potential for diverse cosmological scenarios

Abstract

We propose two new versions of ghost-free generalized $F(R)$ gravity with Lagrange multiplier constraint. The first version of such theory for a particular degenerate choice of the Lagrange multiplier, corresponds to mimetic $F(R)$ gravity. The second version of such theory is just the Jordan frame description of mimetic gravity with potential. As we demonstrate, it is possible to realize several cosmological scenarios in such theory. In particulary, de Sitter solutions may also be found.