Analyzing Conserved Currents in F(R) theory of gravity

TL;DR

This paper critically examines conserved currents in F(R) gravity, revealing that not all previously claimed symmetries satisfy the field equations unless constraints are properly incorporated, and offers a generalized action for cosmological applications.

Contribution

It demonstrates that many conserved currents in F(R) gravity do not satisfy field equations unless constraints are included, and provides a generalized action to address cosmic puzzles.

Findings

Not all conserved currents satisfy field equations without constraints.

A list of F(R) forms with associated conserved currents is provided.

A generalized action is constructed for cosmological implications.

Abstract

F(R) theory of gravity is claimed to admit a host of conserved currents under the imposition of Noether symmetry following various techniques. However, for a constrained system such as gravity, Noether symmetry is not on-shell. As a result, the symmetries do not necessarily satisfy the field equations in general, constraints in particular, unless the generator is modified to incorporate the constraints. In the present manuscript, we apply the first theorem of Poisson to unveil the fact that not all the conserved currents appearing in the literature for F(R) theory of gravity, satisfy the field equations. We also provide a list of available forms of F(R) along with associated conserved currents, and construct a generalized action, which might address the cosmic puzzle, elegantly.