Interaction of dark energy in the anisotropic locally rotationally symmetric (LRS) Bianchi type-I metric is investigated in the context of modified f R , T theory of gravity, where R is the Ricci scalar and T is the trace of stress energy momentum tensor. We choose the particular form of the functional f R , T = f 1 R + f 2 T ; then, we find the exact solutions of the field equations by applying inhomogeneous equation of state, p = ω ρ − Λ t , and a generalized form of hybrid expansion law. The transition of deceleration to acceleration is observed in this model. It is also observed that the universe shows accelerated expansion at late epoch. The derived model overlaps with Λ CDM at late time which is in agreement with present observation. Energy conditions of the derived model are also investigated. From the plot, we observe the age of universe t 0 ≈ 13.821   Gyr for the observed H 0 ≈ 70.07   Kms ‐ 1 Mpc ‐ 1 . The physical and geometrical behaviours of these models are also discussed.

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Despite having a reasonably successful account of accelerated cosmology, understanding of the early evolution of Universe has always been difficult for mankind. Our promising strategy is based on a novel class of symmetric teleparallel theories of gravity called f(Q), in which the gravitational interaction is caused by the non-metricity scalar Q, which may help to solve some problems. We consider the locally rotationally symmetric (LRS) Bianchi type-I spacetime cosmological models and derive the motion of equations to study the early evolution of the cosmos. By assuming the hybrid expansion law (HEL) for the average scale factor, we are able to determine the solutions to the field equations of Bianchi type-I spacetime. We discuss the energy density profile, the equation of state, and the skewness parameter and conclude that our models preserve anisotropic spatial geometry during the early stages of the Universe with the possibility of an anisotropic fluid present. However, as time goes on, even in the presence of an anisotropic fluid, the Universe may move towards isotropy due to inflation while the anisotropy of the fluid dims away at the same time. It is seen from the squared speed of sound that Universe shows phantom nature at the beginning then approaches to dark energy at present epoch. We analyze both geometrical and physical behaviours of the derived model.

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