Emergence of space and the general dynamic equation of Friedmann-Robertson-Walker universe

TL;DR

This paper presents a unified approach to derive Friedmann equations in various gravity theories, including $f(R)$ and deformed Hořava-Lifshitz, supporting the idea that spacetime dynamics emerge from deeper principles.

Contribution

It introduces a unified formula that encompasses different gravity modifications, extending Padmanabhan's emergent spacetime framework to multiple theories.

Findings

Unified formula successfully derives Friedmann equations in multiple gravity theories.

The proposed approach validates the emergent spacetime perspective.

Results support the universality of the dynamic equations across theories.

Abstract

A novel idea that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergent phenomena was proposed by T. Padmanabhan. The Friedmann equations of FRW universe can be derived from different gravity theories with different modifications of Padmanabhan's proposal. In this paper, a unified formula is proposed, in which those modifications can be treated as special cases when the formula is applied to different universe radii. Furthermore, the dynamic equations of FRW universe in the $ f(R) $ theory and deformed Ho{\v{r}}ava-Lifshitz theory are investigated. The results show the validity of our proposed formula.