From five dimensional flat spacetime to our four dimensional braneworld via Kaluza-Klein

Abstract

In five dimensional cosmological models, the convention is to include the fth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be introduced. In our metric ansatz we take the scale factor of three dimensional space, the x; y; z coordinates, to depend on both time and internal space. We allow time and internal space, the extra dimension, to share the same metric coeffiient that depends on both dimensions. As such time and internal space play similar roles. From such a metric, we obtain a five dimensional at spacetime into which all relevant four dimensional cosmologies can be locally embedded. Different cases, such as radiation, matter or dark energy dominated cosmologies, correspond to different choices of the free parameters. Each choice is a different frame. We argue on which frame might correspond to the cosmological frame. From our choice of the cosmological frame we obtain a braneworld scenario by restraining internal space from stretching along the negative direction. In this model all the matter fields are con ned to the brane and the bulk is empty. We also see that it is possible for the three dimensional space to shrink to zero away from the brane. Thus our four dimensional world is confined to this four dimensional brane.