Emergence of cosmic space and the maximization of horizon entropy

TL;DR

This paper explores how the universe's expansion as an emergence process relates to maximizing horizon entropy across various gravity theories, revealing a deep connection between cosmic evolution and thermodynamics.

Contribution

It generalizes the law of emergence to Gauss-Bonnet and Lovelock gravities and demonstrates its consistency with horizon entropy maximization in non-flat universes.

Findings

Both the law of emergence and entropy maximization require an asymptotically de Sitter universe.

Maximum horizon entropy occurs when bulk and surface degrees of freedom are equal.

The connection between emergence law and horizon thermodynamics holds beyond Einstein gravity, regardless of spatial curvature.

Abstract

The spatial expansion of the universe can be described as the emergence of space with the progress of cosmic time, through a simple equation, $\Delta V = \Delta t\left(N_{surf}- N_{bulk}\right)$. This law of emergence suggested by Padmanabhan in the context of general relativity for a flat universe has been generalized by Sheykhi to Gauss Bonnet and Lovelock gravity for a universe with any spacial curvature. We investigate whether this generalized holographic equipartition effectively implies the maximization of horizon entropy. First, we obtain the constraints imposed by the maximization of horizon entropy in Einstein, Gauss Bonnet and Lovelock gravities for a universe with any spacial curvature. We then analyze the consistency of the law of emergence in \cite{Sheykhi}, with these constraints obtained. Interestingly, both the law of emergence and the horizon entropy maximization demands an asymptotically de Sitter universe with $\omega \geq -1$. More specifically, when the degrees of freedom in the bulk $( N_{bulk})$ becomes equal to the degrees of freedom on the boundary surface $(N_{surf}),$ the universe attains a state of maximum horizon entropy. Thus, the law of emergence can be viewed as a tendency for maximizing the horizon entropy, even in a non flat universe. Our results points at the deep connection between the law of emergence and horizon thermodynamics, beyond Einstein gravity irrespective of the spacial curvature.