مشخصات پژوهش

According to Padmanabhan’s proposal, the dif-ference 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  V /t = N sur − N bulk whereN bulk and N sur are referred to the degrees of freedom related to the matter and energy con-tent inside the bulk and surface area, respectively (Padman-abhan, 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 free-dom. Considering the modification of the Friedmann equa-tions 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 geom-etry of the brane embedded in higher-dimensional spacetime as  V /t = N sur − N bulk − N extr where N extr is for the degree of freedom related to the extrinsic geometry of the brane, whileN sur and N bulk are defined as before. Finally, we study the validity of the first and second laws of thermo-dynamics 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