O'Hanlon actions by Noether symmetry

TL;DR

This paper explores the relationship between Brans-Dicke and O'Hanlon actions through conformal symmetry, demonstrating how Noether symmetry is preserved and identifying potentials that respect this symmetry in both frameworks.

Contribution

It establishes a method to find Noether-symmetric potentials in O'Hanlon actions based on known symmetries in Brans-Dicke actions via conformal transformations.

Findings

Noether symmetry is preserved under conformal transformations.

Potentials respecting Noether symmetry in Brans-Dicke actions correspond to those in O'Hanlon actions.

The approach simplifies identifying symmetric potentials in scalar-tensor theories.

Abstract

By using the conformal symmetry between Brans-Dicke action with $\omega=-\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials respecting Noether symmetry in O'Hanlon action in Einstein frame.