TL;DR
This paper derives a general five-dimensional solution that induces a flat universe cosmology on a three-brane, linking brane metrics to higher-dimensional spacetimes and embedding standard cosmologies within orbifold models.
Contribution
It provides a new general solution for five-dimensional orbifold spacetimes inducing flat cosmologies on three-branes, including explicit embeddings for inflationary and radiation-dominated universes.
Findings
Derived expressions for energy density and pressure on the brane.
Constructed five-dimensional spacetimes for given brane metrics.
Embedded standard cosmologies within orbifold spacetimes.
Abstract
In this paper a general solution is found for a five dimensional orbifold spacetime that induces a cosmology on a three-brane. Expressions for the energy density and pressure on the brane in terms of the brane metric are derived. Given a metric on the brane it is possible to find five dimensional spacetimes that contain the brane. This calculation is carried out for an inflationary universe and for a metric that corresponds to a radiation dominated universe in standard cosmology. It is also shown that any cosmology can be embedded in a flat five dimensional orbifold spacetime and the equation of the three-brane surface is derived. For an inflationary universe it is shown that the surface is the usual hyperboloid representation of de Sitter space, although it is embedded in an orbifold spacetime.
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