Friedmann equations in braneworld scenarios from emergence of cosmic space

TL;DR

This paper derives Friedmann equations for braneworld cosmologies using a new emergent space perspective, extending to Gauss-Bonnet corrections and nonflat universes, linking spacetime dynamics to degrees of freedom.

Contribution

It applies the emergent space approach to derive Friedmann equations in braneworld and Gauss-Bonnet scenarios, including nonflat universes, which is a novel extension.

Findings

Derived Friedmann equations for braneworlds with arbitrary curvature.

Extended the approach to Gauss-Bonnet braneworlds with curvature corrections.

Included nonflat universe cases in the emergent space framework.

Abstract

Recently, it was argued that the spacetime dynamics can be understood by calculating the difference between the degrees of freedom on the boundary and in the bulk in a region of space. In this Letter, we apply this new idea to braneworld scenarios and extract the corresponding Friedmann equations of $(n-1)$-dimensional brane embedded in the $(n+1)$-dimensional bulk with any spacial curvature. We will also extend our study to the more general Gauss-Bonnet braneworld with curvature correction terms on the brane and in the bulk, and derive the dynamical equation in a nonflat Universe.