Generalized Holographic Equipartition for Friedmann-Robertson-Walker Universes

TL;DR

This paper extends the holographic equipartition concept to derive Friedmann equations for FRW universes with various curvatures in higher-dimensional gravity theories, supporting the holographic perspective of cosmic expansion.

Contribution

It provides a generalized expression for holographic equipartition applicable to different gravity theories and spatial curvatures, broadening the scope of Padmanabhan's idea.

Findings

Derived Friedmann equations for curved FRW universes in higher-dimensional Einstein, Gauss-Bonnet, and Lovelock gravity.

Established the validity of holographic equipartition in diverse gravitational frameworks.

Demonstrated the consistency of the generalized approach with known cosmological equations.

Abstract

The novel idea that spatial expansion of our universe can be regarded as the consequence of the emergence of space was proposed by Padmanabhan. By using of the basic law governing the emergence, which Padmanabhan called holographic equipartition, he also arrives at the Friedmann equation in a flat universe. When generalized to other gravity theories, the holographic equipartition need to be generalized with an expression of $f(\Delta N,N_{sur})$. In this paper, we give general expressions of $f(\Delta N,N_{sur})$ for generalized holographic equipartition which can be used to derive the Friedmann equations of the Friedmann-Robertson-Walker universe with any spatial curvature in higher (n+1)-dimensional Einstein gravity, Gauss-Bonnet gravity and more general Lovelock gravity. The results support the viability of the perspective of holographic equipartition.