Dimensional reduction in 6D standing waves braneworld

Abstract

We found cosmological solution of the 6D standing wave braneworld model generated by gravity coupled to a massless scalar phantom-like field. By obtaining a full exact solution of the model we found a novel dynamical mechanism in which the anisotropic nature of the primordial metric gives rise to expansion of three spatial brane dimensions and affectively reduction of other spatial directions. This dynamical mechanism can be relevant for dimensional reduction in string and other higher dimensional theories in the attempt of getting a 4D isotropic expanding space-time. Braneworld models with large extra dimensions [1, 2] have been very useful in addressing several problems in high energy physics (for reviews see [3]). Most of the braneworlds are realized as time-independent configurations, however, mostly within the framework of cosmological studies, there have been proposed models that employ time-dependent metrics and matter fields [4]. Recently was proposed novel non-stationary braneworld generated by standing gravitational waves minimally coupled to a bulk scalar field [5][6][7]. In this paper we study cosmological solution to the specific 6D standing waves braneworld [7] involved a phantom-like scalar fields. In our model the phantom scalar field is present only in the bulk and does not couple to ordinary matter on the brane (to avoid the well-known problems of stability which occur with ghost fields).We consider 6D space-time, having the signature (+, −, −, −, −, −), with a non-self interacting phantom-like scalar field coupled to gravity: