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

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