Friedmann equations and emergence of cosmic space

TL;DR

This paper examines Padmanabhan's conjecture on the emergence of cosmic space, confirming its validity for flat universes in Einstein gravity and highlighting limitations in non-flat cases, with implications for holographic and energy principles.

Contribution

It demonstrates the conditions under which Padmanabhan's conjecture holds and critiques previous extensions to non-Einstein and non-flat universes.

Findings

Conjecture holds for flat FRW universe in Einstein gravity.

Fails for non-flat universe unless using aerial volume.

Highlights shortcomings in previous non-Einstein, non-flat extensions.

Abstract

In this paper, we show that Padmanabhan's conjecture for the emergence of cosmic space [arXiv:1206.4916] holds for the flat Friedmann-Robertson-Walker universe in Einstein gravity but does not hold for the non-flat case unless one uses the aerial volume instead of the proper volume. Doing this, we also show that various works extending Padmanabhan's conjecture to non-Einstein and non-flat cases have serious shortfalls. This analysis is done using the Friedmann equation with the further assumptions of the holographic principle and the equipartition rule of energy.