  Padmanabhan in his paper [arxiv: 1206.4916] put forth an intriguing idea
arguing that the accelerated expansion of the universse can be viewed as the
emergence of cosmic space as cosmic time progresses, with the expansion
triggered due to the difference in the degrees of freedom on a holographic
surface and the one in its emerged bulk. We show that the modified expansion
law of the universe proposed by Sheykhi in a non-flat Friedmann-
Robertson-Walker (FRW) universe and by Cai in a flat FRW universe could be
derived starting from the first law of thermodynamics, in (n+1) dimensional
Einstein gravity, Gauss-Bonnet and more general Lovelock gravity theories. We
have also derived the modified versions of the expansion law for a flat
universe due to Yang et al, in the case of Gauss-Bonnet and Lovelock gravities,
from the first law of thermodynamics. This approach is unique in the sense that
all these modified versions of the expansion law is derived from a
thermodynamic identity that has the same form regardless of the gravity theory
and irrespective of whether the universe is flat or non-flat
