Hidden conformal symmetry of smooth braneworld scenarios

Abstract

In this paper, we generalize our previous model ( arXiv:1705.09331 ), on a hidden conformal symmetry of smooth braneworld scenarios, to the case with two real scalar fields non-minimally coupled to gravity. The gauge condition reduces the action of the system to the action where gravity minimally couples to one of the scalar fields, plus a cosmological constant. We show that, depending on the internal symmetry of the scalar fields, the two possibilities, SO(2) or SO(1, 1), emerge. In the SO(2) case, we get a ghost-like scalar field action, which can describe two models — Standing Wave and Sine-Gordon smooth braneworlds. For the SO(1, 1) case we get the standard sign for the kinetic part of the scalar field. By breaking the SO(1, 1) symmetry (but keeping the conformal one) we are able to get two Randall–Sundrum models, with a non-minimal coupling and with a scalar field having hyperbolic potential. We conclude that this method can be seen as a solution-generating technique and a natural way to introduce nontrivial scalar fields that can provide smooth braneworld models.