Scalar tensor theory of gravity carrying a conserved current

TL;DR

This paper explores a scalar-tensor gravity theory with a conserved current linked to specific potential and coupling functions, enabling analysis of symmetries across various gravity models.

Contribution

It establishes a conserved current in scalar-tensor gravity theories under specific potential and coupling conditions, connecting arbitrary parameters and enabling symmetry exploration.

Findings

Conserved current exists when potential is proportional to the square of the coupling function.

The conserved current relates the coupling functions f(φ) and ω(φ).

Framework allows analysis of symmetries in standard and nonstandard gravity models.

Abstract

A general scalar-tensor theory of gravity carries a conserved current for a trace free minimally coupled scalar field, under the condition that the potential $V(\phi)$ of the nonminimally coupled scalar field is proportional to the square of the parameter $f(\phi)$ that is coupled with the scalar curvature $R$. The conserved current relates the pair of arbitrary coupling parameters $f(\phi)$ and $\omega(\phi)$, where the latter is the Brans-Dicke coupling parameter. Thus fixing up the two arbitrary parameters by hand, it is possible to explore the symmetries and the form of conserved currents corresponding to standard and many different nonstandard models of gravity.