Vacuum Energy in Saez-Ballester Theory and Stabilization of Extra Dimensions

Abstract

In this work, we study a spherically symmetric metric in 5D within the framework of Saez-Ballester Theory, where minimal dark energy-matter interaction occurs. We predict that the expanding isotropic universe will be progressively DE dominated. We estimate few values of the deceleration parameter, very close to the recently predicted values. We obtain the value of the DE EoS parameter as ω=−1. Additionally, we measure the value of the overall density parameter as Ω=0.97(≈1), in line with the notion of a close to or nearly (not exactly) flat universe. We predict that the model universe starts with the Big-Bang and ends at the Big Freeze singularity. In general, we cannot find conditions for stabilization of extra dimensions in general relativity, and all dimensions want to be dynamical. Here, we present two possible conditions to solve this stabilization problem in general relativity.

Five-Dimensional Cosmological Model with One Dimensional Cosmic String Coupled with Zero Mass Scalar Field in Lyra Manifold

“…Kiran et al [12] discussed spatially homogeneous and anisotropic Bianchi type-III bulk viscous fluid string cosmological model in gravity. Singh et al [13] considered a five-dimensional spherically symmetric space-time within the framework of Saez-Ballester theory, wherever minimal dark energy-matter interaction occurs. Bhabor et al [14] studied fivedimensional Bianchi type-I string cosmological models with bulk viscous fluid in Lyra geometry.…”

Noncompactified Kaluza–Klein Gravity

“…In contrast to the latter, the SB theory includes the action of ordinary matter that is not coupled to the SB scalar field. Various cosmological models have been established in the context of the SB theory to study open problems in both the classical and quantum regimes [49][50][51][52][53][54]. Applying the similar reduction procedure used to construct the MBDT, without assuming the presence of the higher dimensional matter fields and imposing the cylindricity condition on the extra coordinate, it has been shown that the SB field equations associated to the bulk split into four sets of effective field equations on any hypersurface orthogonal to the extra dimension [9].…”