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 in the model is proportional to the shear scalar 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 is a decreasing function of cosmic time in Lyra’s geometry, and for late times, the gauge function 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 CDM cosmological model in late times and consistent with the recent observations of cosmological data.

中文翻译：

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广义相对论和Lyra几何中的Bianchi V型全息暗能量模型分析

在广义相对论和Lyra几何的框架下，我们在存在暗物质和全息暗能量模型成分的情况下，分析了各向异性且均匀的Bianchi V型时空。通过考虑两种具体情况获得了微分方程场的解，即模型中的膨胀标量与剪切标量成比例并将平均比例因子作为混合膨胀形式。在广义相对论和天琴座几何中获得了场方程的解。获得并比较了两种性质的暗物质的能量密度，因此广义相对论中的暗物质的能量密度与天琴座几何中的暗物质的能量密度略有不同。在各个框架中，压力和全息暗能量模型的EoS参数都发生了类似的行为。此外，可以得出结论，在两个框架中，诸如平均哈勃参数，空间体积，各向异性参数，膨胀标量和剪切标量等物理参数是相同的。此外，观察到量规功能是天琴座几何中宇宙时间的递减函数，并且在后期，轨距函数收敛到零，而天琴座几何在所有方面都减小到广义相对论。最后，我们得出的结论是，我们的模型在后期与CDM宇宙学模型非常相似，并且与最近对宇宙学数据的观察一致。