Emergent Universe in the Braneworld Scenario

TL;DR

This paper explores how the extrinsic geometry of a brane in higher dimensions influences the universe's expansion, modifying Padmanabhan's degrees of freedom relation and examining thermodynamic laws in this context.

Contribution

It introduces a correction term accounting for extrinsic geometry in Padmanabhan's framework within braneworld scenarios, extending the understanding of universe dynamics.

Findings

Derived a modified degrees of freedom relation including extrinsic geometry.

Analyzed the impact of extrinsic geometry on universe acceleration.

Confirmed the validity of thermodynamic laws in the braneworld context.

Abstract

According to Padmanabhan's proposal, the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space may result in the acceleration of Universe expansion through the relation $\Delta V/\Delta t = N_{\rm sur}-N_{\rm bulk}$ where $N_{\rm bulk}$ and $N_{\rm sur}$ are referred to the degrees of freedom related to the matter and energy content inside the bulk and surface area, respectively \cite{Pad1}. In this paper, we study the dynamical effect of the extrinsic geometrical embedding of an arbitrary four dimensional brane in a higher dimensional bulk space and investigate the corresponding degrees of freedom. Considering the modification of Friedmann equations arising from a general braneworld scenario, we obtain a correction term in Padmanabhan's relation, denoting the number of degrees of freedom related to the extrinsic geometry of the brane embedded in higher dimensional spacetime as $\Delta V /\Delta t=N_{\rm sur}-N_{\rm bulk}-N_{\rm extr}$ where $N_{\rm extr}$ is referred to the degree of freedom related to the extrinsic geometry of the brane while $N_{\rm sur}$ and $N_{\rm bulk}$ are as well as before. Finally, we study the validity of the first and second laws of thermodynamics for this general braneworld scenario in the state of thermal equilibrium and in the presence of confined matter fields to the brane with the induced geometric matter fields.