The paper deals with the investigation of a homogeneous and anisotropic space-time described by Bianchi type III metric with perfect fluid in Lyra geometry setting. Exact solutions of the Einsten's field equations have been obtained under the assumption of quadratic equation of state (EoS) of the form p = aρ 2 − ρ , where a is a constant and strictly a > 0. The physical and geometrical aspects are also examined in details. AbstractThe paper deals with the investigation of a homogeneous and anisotropic space-time described by Bianchi type III metric with perfect fluid in Lyra geometry setting. Exact solutions of the Einsten's field equations have been obtained under the assumption of quadratic equation of state (EoS) of the form p = aρ 2 − ρ , where a is a constant and strictly a > 0. The physical and geometrical aspects are also examined in details.

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With due consideration of reasonable cosmological assumptions within the limit of the present cosmological scenario, we have analysed a spherically symmetric metric in 5D setting within the framework of Lyra manifold. The model universe is predicted to be a DE model, dominated by vacuum energy. The model represents an oscillating model, each cycle evolving with a big bang and ending at a big crunch, undergoing a series of bounces. The universe is isotropic and undergoes super-exponential expansion. The value of Hubble's parameter is measured to be H = 67.0691 which is very close to H0 = 67.36±0.54kms −1 M pc −1 , the value estimated by the latest Planck 2018 result. A detailed discussion on the cosmological parameters obtained is also presented with graphs.

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.

We consider it worthy if we could construct a realistic model universe that would enable us to identify a clue about the source of dark energy. So, we develop a Scale Covariant Theory model universe considering a 5D spherically symmetric space-time. It is predicted that the constructed model itself behaves as a phantom energy model/source that tends to a de Sitter phase avoiding the finite-time future singularity (big rip). The model universe is isotropic and is free from an initial singularity. The gravitational constant [Formula: see text] decreases with a variation of [Formula: see text][Formula: see text]yr[Formula: see text] and the Hubble parameter is estimated to be [Formula: see text]. We also provide a thorough analysis of the cosmological findings with graphical representations.