# Cosmic acceleration via space-time-matter theory

## TL;DR

This paper explores how a five-dimensional space-time-matter theory can explain the universe's late-time acceleration, deriving equations and observable predictions consistent with an accelerating universe.

## Contribution

It introduces a model where the extra dimension's scale factor varies linearly with redshift, leading to late-time cosmic acceleration within STM theory.

## Key findings

- The model predicts an accelerating universe consistent with observations.
- Derived geodesic deviation equations for STM theory.
- Compared observer area-distance with other cosmological models.

## Abstract

We consider the space-time-matter theory (STM) in a five-dimensional vacuum space-time with a generalized FLRW metric to investigate the late-time acceleration of the universe. For this purpose, we derive the four-dimensional induced field equations and obtain the evolution of the state parameter with respect to the redshift. Then, we show that with consideration of the extra dimension scale factor to be a linear function of redshift, this leads to a model which gives an accelerating phase in the universe. Moreover, we derive the geodesic deviation equation in the STM theory to study the relative acceleration of the parallel geodesics of this space-time, and also, obtain the observer area-distance as a measurable quantity to compare this theory with two other models.