EXACT SOLUTIONS OF EMBEDDING THE 4D UNIVERSE IN A 5D EINSTEIN MANIFOLD

Abstract

One of the simplest ways to extend 4D cosmological models is to add another spatial dimension to make them 5D. In particular, it has been shown that the simplest of such 5D models, i.e. one in which the right-hand side of the Einstein equation is empty, induces a 4D nonempty universe. Accordingly, the origin of matter in a real 4D universe might be mathematically attributed to the existence of one (fictitious) extra spatial dimension. Here we consider the case of an empty 5D universe possessing a cosmological constant Λ and obtain exact solutions for both positive and negative values of the Λ. It is seen that such a model can naturally reduce to a power law ΛCDM model for the real universe. Further, it can be seen that the arbitrary constants and functions appearing in this model are endowed with definite physical meanings.