Analysis of Bianchi Type V Holographic Dark Energy Models in General Relativity and Lyra’s Geometry

Abstract

In this paper, we analyze anisotropic and homogeneous Bianchi type V spacetime in the presence of dark matter and holographic dark energy model components in the framework of general relativity and Lyra’s geometry. The solutions of differential equation fields have been obtained by considering two specific cases, namely, the expansion scalar θ in the model is proportional to the shear scalar σ and the average scale factor taken as hybrid expansion form. The solutions for field equations are obtained in general relativity and Lyra’s geometry. The energy density of dark matter in both natures was obtained and compared so that the energy density of dark matter in general relativity is slightly different from the energy density of dark matter in Lyra’s geometry. A similar behavior occurred in case of pressure and EoS parameter of holographic dark energy model in respective frameworks. Also, it is concluded that the physical parameters such as the average Hubble parameter, spatial volume, anisotropy parameter, expansion scalar, and shear scalar are the same in both frameworks. Moreover, it is observed that the gauge function β t is a decreasing function of cosmic time in Lyra’s geometry, and for late times, the gauge function β t converges to zero and Lyra’s geometry reduces to general relativity in all respects. Finally, we conclude that our models are a close resemblance to the Λ CDM cosmological model in late times and consistent with the recent observations of cosmological data.

Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

“…In order to study the anisotropic inflationary phase, we have evaluated the values of some parameters for an anisotropic universe, e.g., expansion scalar (θ), anisotropy parameter (Δ), the shear scalar (σ), and deceleration parameter (q) in both cases. As seen in figures 1(a), (b) (m ≠ n case), and in figures 5(a), (b) (m= n case), the values of the anisotropy parameter (Δ) and the shear scalar (σ) are large at the initial epoch (t → 0) and become negligible at t → ∞ , suggesting that the Universe expands isotropically at later times, which is consistent with the studies of [53][54][55][56][57]. We have shown that in this model the values of the ratio of shear scalar to expansion scalar ( H 0 ( ) s ) lie well within the observed range (52) as predicted in [25].…”

“…Because of this, just like in the m ≠ n case, the parameters Δ, σ are diminishing functions of time, becoming infinite at t → 0 and disappearing at t → ∞ . This implies that, after a considerable amount of time, this model isotropizes the Universe in this case as well, which is similar to the investigations of [53][54][55][56][57].…”

“…The parameters Δ, σ are therefore decreasing functions of time, becoming infinite at t → 0 and disappearing at t → ∞ . As a result, the model isotropizes over a long period of time, suggesting that the Universe will eventually spread isotropically, which resembles with the investigations of [53][54][55][56][57].…”

A Study of Evolution of Cosmological Parameters Based on a Dark Energy Model in the Framework of Brans-Dicke Gravity

“…Negative pressure is associated with DE, causing the accelerated expansion of the universe. This behavior is consistent with the findings of several studies [37,38]. Positive values for 𝑗 and 𝑙 and negative values for 𝑠 represent accelerated expansion [39].…”

Bianchi Type-II Fractional Cosmological Model with Variable Lambda

“…They discovered that an accelerated expansion period isotropizes both the expansion anisotropy and the anisotropy of the fluid. A host of authors have investigated spatially homogeneous and anisotropic DE models both in general relativity and in modified theories of gravitation (See [15], [21], [26], [31]).…”