Emergent universe in the braneworld scenario

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-sur - N-bulk where N-bulk and N-sur are referred to the degrees of freedom related to the matter and energy content inside the bulk and surface area, respectively (Padmanabhan, arXiv:1206.4916v1, 2012). 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 the 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 space-time as Delta V/Delta t = N-sur - N-bulk - N-extr where N-extr is for the degree of freedom related to the extrinsic geometry of the brane, while N-sur and N-bulk are defined 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.