Expansion Law From First Law of Thermodynamics

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