Analyzing conserved currents in F(R) theory of gravity

Abstract

[Formula: see text] 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 this paper, we apply the first theorem of Poisson to unveil the fact that not all the conserved currents appearing in the literature for [Formula: see text] theory of gravity satisfy the field equations. We also provide a list of available forms of [Formula: see text] along with associated conserved currents and construct a generalized action, which might address the cosmic puzzle, elegantly.

Inflation with F(T) teleparallel gravity

“…Thus, Gravity is a constrained system, and Noether symmetry is not on-shell for such a constrained system, and every available Noether symmetry of gravitational theory, is required to satisfy the four aforesaid equations [60][61][62]. Alternatively, application of (modified) Poisson first theorem happens to be a straight forward technique to check consistency, in this regard [63,64]. In F (T ) gravity theory however, apart from the metric coefficients, the configuration space is spanned by (T, Ṫ ).…”

A viable form of teleparallel F(T) theory of gravity

“…It is to be mentioned that for the isotropic and homogeneous model (6), only the energy constraint equation survives, which has to be satisfied by the symmetry equation. Application of (modified) Poisson first theorem happens to be a straight forward technique to examine such consistency in this regard [67,68]. For F(R) theory of gravity, a host of Noether symmetries were claimed and only a few, presented in Table 1, survived after such consistency check.…”