Entropy Maximization in the Emergent Gravity Paradigm

The accelerated expansion of the universe can be interpreted as a quest for satisfying holographic equipartition. It can be expressed by a simple law, $\Delta V = \Delta t\left(N_{surf}- N_{bulk}\right)$ which leads to the standard Friedmann equation. This novel idea suggested by Padmanabhan in the context of general relativity has been generalized by Cai and Yang et al. to Gauss-Bonnet and Lovelock gravities for a spatially flat universe in different methods. We investigate the consistency of these generalizations with the constraints imposed by the maximum entropy principle. Interestingly, both these generalizations imply entropy maximization even if their basic assumptions are different. Further, we analyze the consistency of Verlinde's emergent gravity with the maximum entropy principle in the cosmological context. In particular, we consider the generalization suggested by Shu and Gong, in which an energy flux through the horizon is assumed, in addition. Even though the conceptual formulations are different, these two emergent perspectives of gravity describes a universe which behaves as an ordinary macroscopic system. Our results provide further support to the emergent gravity paradigm.