On the Friedmann Equation in Brane-World Scenarios

TL;DR

This paper derives the Friedmann equation in brane-world models from a four-dimensional Brans-Dicke theory, showing how the quadratic energy density dependence and dark radiation term arise, and confirms the consistency of the radiation era with nucleosynthesis.

Contribution

It demonstrates a derivation of the brane-world Friedmann equation from standard four-dimensional theory, clarifying the origin of dark radiation and quadratic energy density dependence.

Findings

Dark radiation depends linearly on brane energy densities.

Radion evolution leads to a standard radiation-dominated era.

Cosmology is consistent with nucleosynthesis constraints.

Abstract

The Friedmann law on the brane generically depends quadratically on the brane energy density and involves a ``dark radiation'' term due to the bulk Weyl tensor. Despite its unfamiliar form, we show how it can be derived from a standard four-dimensional Brans-Dicke theory at low energy. In particular, the dark radiation term is found to depend linearly on the brane energy densities. For any equation of state on the branes, the radion evolves such as to generate radiation-dominated cosmology. The radiation-dominated era is conventional and consistent with nucleosynthesis.