Cosmic acceleration via space-time-matter theory

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.

Cosmic acceleration and geodesic deviation in chameleon scalar field model

“…where A 0 is the area of the object and Ω 0 is the solid angle [74,75]. In this respect, using the relation |d/dl| = E −1 0 (1 + z) −1 d/dν = H (1 + z) d/dz, wherein dl = a (t) dr, while assuming that the deviation vector to be zero at z = 0, relation (4.34) yields 2 with the corresponding ones in the ΛCDM model [75], the f (R) theory [84], the Hu-Sawicki models [85], the f (R, T ) theory [30], the Brans-Dicke theory [78] and the space-time-matter theory [33] indicates that the general behavior of the null geodesic deviation and the observer area-distance in the chameleon model are similar to these models. The similarity of our results to the corresponding ones in the ΛCDM model reveals that the chameleon model remains phenomenologically viable and can be tested with the observational data [75].…”