Role of Extra Dimension in Accelerated Expansion

Abstract

A five-dimensional FRW-type Kaluza–Klein cosmological model is taken to study the role of extra dimension in the expansion of the universe. Relation between scale factors corresponding to conventional four dimensions and the extra dimension has been established. Field equations are solved in order to find out the effect of pressure corresponding to these scale factors. Conditions for accelerated expansion are derived.

Static Extra Dimension and Acceleration of the Universe

“…Further, it is now well established that the universe is accelerating in the present epoch [14,15]. To consider the phenomenon of acceleration of the universe some researchers have suggested that this acceleration is due to the cosmological constant or dark energy [16][17][18].…”

A Cosmological Model with Static Extra Dimensions and Varying Cosmological Constant

“…We have already found the solution of field equations by taking the direct proportionality between the pressures corresponding to the usual four dimensions and the extra dimension [54,55]. Our results were extended in reference [39] by taking a fixed cosmological constant.…”

“…In our earlier work [54,55] we had shown that the extra dimension plays an important role in acceleration of the universe. On the other hand, it is also known that the cosmological constant is always corresponds to a negative pressure.…”

“…where t, r a , r b , θ, ϕ, and are the components of the five dimensional space-time coordinate The Riemannian tensor and Ricci scale for the metric given by (1) can be calculated easily [54,55]. The Einstein's field equation with cosmological constant is given as below,…”

“…the extra dimensions) which contributes in the acceleration of the universe [52][53][54][55][56][57]. So it is important to look for a cosmological model with varying Λ and extra dimensions.…”