Duality transformation and conformal equivalent scalar-tensor theories

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.

6 pages, no figures, minor revision, to appear in MPLA

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Cited by in corpus (7)

• Selected topics in scalar-tensor theories and beyond
• Conservation laws and Exact Solutions in Brans-Dicke Cosmology with a Scalar Field
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Infinite dimensional symmetry groups of the Friedmann equations
• A new symmetry of the spatially flat Einstein-Friedmann equations
• An issue with the classification of the scalar-tensor theories of gravity
• $O(d,d)$ symmetry in teleparallel dark energy