Duality transformation and conformal equivalent scalar-tensor theories

TL;DR

This paper investigates the duality symmetry of the Dilaton field in cosmology, showing how conformal transformations affect this symmetry and uncovering related conservation laws and mathematical equivalences.

Contribution

It identifies conformal equivalent theories to the Dilaton field and analyzes the impact of conformal transformations on Gasperini-Veneziano duality symmetry.

Findings

Duality symmetry does not survive conformal transformations.

Shared conservation law of Noetherian type among the theories.

Equivalence of the Dilaton Lagrangian to a hyperbolic oscillator in Lorentzian space.

Abstract

We deal with the duality symmetry of the Dilaton field in cosmology and specifically with the so-called Gasperini-Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the Dilaton field, and we show that under conformal transformations Gasperini-Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the Dilaton field. Finally, we show that the Lagrangian of the Dilaton field is equivalent with that of the two-dimensional \textquotedblright hyperbolic oscillator\textquotedblright\ in a Lorentzian space whose $O(d,d)$ invariance is transformed to the Gasperini-Veneziano duality invariance in the original coordinates.