• Duality transformation and conformal equivalent scalar–tensor theories

      Gionti, Gabriele; Paliathanasis, Andronikos; Univ Arizona, Steward Observ (WORLD SCIENTIFIC PUBL CO PTE LTD, 2018-05-30)
      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 the two-dimensional "hyperbolic oscillator" in a Lorentzian space whose O(d, d) invariance is transformed into the Gasperini-Veneziano duality invariance in the original coordinates.