New conserved tensors and Brans-Dicke type field equation, using integrability condition

TL;DR

This paper introduces new conserved tensors for scalar fields in Minkowski space, derives Brans-Dicke type field equations without the principle of equivalence, and extends to modified gravity theories using integrability conditions.

Contribution

It presents novel off-shell and on-shell conserved quantities for scalar fields and derives Brans-Dicke and modified gravity field equations from integrability conditions.

Findings

New conserved tensors related to scalar field kinematics.

Derivation of Brans-Dicke type equations without equivalence principle.

Field equations for modified gravity from curvature scalar.

Abstract

We explore some new off-shell and on-shell conserved quantities for a scalar field in Minkowski space, using integrability condition. The off-shell conserved tensors are related to the kinematics of the field, while a linear combination of the off-shell and the on-shell conserved tensors ends up with the energy-momentum tensor for the scalar field. In the curved background, using Ricci and Bianchi identities, Brans-Dicke type field equations emerge, without requiring the principle of equivalence. Further, starting from the curvature scalar and using these identities, the field equations for modified gravity (Einstein-Hilbert action in the presence of higher-order terms) follows.