|
Abstract
|
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
|