Emergent Friedmann equation from the evolution of cosmic space revisited

TL;DR

This paper extends the emergent space approach to derive the Friedmann equation for nonflat universes, revealing the necessity of a time-dependent Planck constant and highlighting the physical implications of spatial curvature.

Contribution

It generalizes the emergent space framework to nonflat universes and introduces a time-dependent Planck constant to maintain the evolution equation's form.

Findings

The approach applies to nonflat universes, including open and closed models.

A divergence in the Planck constant occurs for open universes with negative curvature.

Physical consequences of spatial curvature are discussed.

Abstract

Following the recent study on the emergent Friedmann equation from the expansion of cosmic space for a flat universe, we apply this method to a nonflat universe, and modify the evolution equation to lead to the Friedmann equation. In order to maintain the same form with the original evolution equation, we have to define the time-dependent Plank constant, which shows that the spatial curvature of $k=0$ and $k=1$ is preferable to $k=-1$ since the Plank constant of the nonflat open universe is divergent. Finally, we discuss its physical consequences.