Einstein and Jordan-Frame Covariant Hamiltonians for F(R) Gravity and Their Canonical Relationships

TL;DR

This paper develops a covariant canonical formalism for F(R) gravity in the Einstein frame, establishes a canonical transformation between Jordan and Einstein frames, and derives the associated generating function.

Contribution

It introduces a covariant Hamiltonian framework for F(R) gravity and explicitly constructs the canonical transformation between Jordan and Einstein frames.

Findings

Derived covariant Hamiltonians in Einstein frame.

Established canonical transformation between frames.

Identified the generating function for the transformation.

Abstract

This paper is devoted to the analysis of the covariant canonical formalism of $F(R)$ gravity in Einstein frame. We also find canonical transformation between covariant canonical formulation of F(R) gravity in Jordan frame and Einstein frames and we also determine corresponding generating function.