A five dimensional model with a fifth dimension as fundamental as time in terms of a cosmological approach

In five dimensional cosmological models, the convention is to include the fifth 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. With such an internal space, we are able to obtain accelerated expansion without introducing dark energy. We obtain a five dimensional flat, meaning both Ricci flat and conformally flat, spacetime into which all relevant four dimensional cosmologies can be locally embedded. We also argue on the choice of the cosmological frame. The choice that is simplest and most convenient in terms of dimensional analysis, amounts to a linearly expanding universe.