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 socalled 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 "hyperbolic oscillator" in a Lorentzian space whose O(d, d) invariance is transformed to the Gasperini-Veneziano duality invariance in the original coordinates. 95.35.+d, 95.36.+x

Multi-fluid cosmology in Einstein gravity: analytical solutions

“…A connection has been made between Einstein-Friedmann equations and methods of supersymmetric quantum mechanics [316,348,349]. As in other areas of physics, also in FLRW cosmology Lie, Noether, and other symmetries are often studied with the ultimate goal of generating first integrals of motion and exact solutions [41,68,88,89,91,92,108,121,122,154,190,319,320,[322][323][324]334,392,423], sometimes in relation with Penrose's cyclic time cosmologies or conformal time [53][54][55]397]. The existence of such a symmetry does not automatically make the corresponding solution a physical one.…”

Selected topics in scalar–tensor theories and beyond

“…52 That the controversy has not been resolved yet is clear from the amount of yearly work on the issue where there is no agreement on the correct answer to these questions. [577][578][579][580][581][582][583][584][585][586][587][588][589][590][591][592][593][594][595] In this section we shall discuss on the conformal frames' issue from the classical point of view exclusively. For a related discussion based on quantum arguments we recommend Refs.…”

An issue with the classification of the scalar–tensor theories of gravity

“…There are known classifications of the different works of different authors and of the same author on this issue [39]. That the controversy has not been resolved yet is clear from the amount of yearly work on the issue where there is no agreement about the correct answer to these questions [110][111][112][113][114][115][116][117][118][119][120][121][122][123][124][125]. Here we shall approach to the conformal frames' issue from the classical standpoint exclusively.…”