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.
Highlights
The relatively recent discovery of the present acceleration of our universe is strictly proved by the astronomical observation of type Ia supernova [1, 2], galaxy redshift survey [3], and cosmic microwave background radiation (CMBR) data [4, 5] which convincingly suggest that the rate of expansion of our universe is positive, i.e., we live in an accelerating expanding universe
We have studied anisotropic and homogeneous Bianchi type V universe filled with dark matter and holographic dark energy in the framework of general relativity and Lyra’s geometry
The solutions for field equations of cosmological models are obtained in general relativity and Lyra’s geometry by using two specific cases: firstly by taking the expansion scalar ðθÞ in the model is proportional to the shear scalar ðσÞ as considered by Thorne [38] and Collins et al [39] and secondly by using the average scale factor as hybrid expansion form
Summary
The relatively recent discovery of the present acceleration of our universe is strictly proved by the astronomical observation of type Ia supernova [1, 2], galaxy redshift survey [3], and cosmic microwave background radiation (CMBR) data [4, 5] which convincingly suggest that the rate of expansion of our universe is positive, i.e., we live in an accelerating expanding universe. Sen [23] proposed a new scalar tensor theory of gravitation They constructed an analog of Einstein’s field equations based on Lyra’s geometry which is in normal gauge. Halford [24] has shown that the constant displacement vector field in Lyra’s geometry plays the role of cosmological constant Λ in general relativity He has shown that the scalar-tensor analysis based on Lyra’s geometry suggests the same effects, within observational limits, as in Einstein’s theory [20]. Motivated by the abovementioned investigations, we have considered the homogeneous Bianchi type V holographic dark energy cosmological models in general relativity and Lyra’s geometry.
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