Mathematical Models and Methods on Higher Dimensional Bulk Viscous String Cosmology with the Framework of Lyra Geometry

We investigate a cosmological scenario generated by a cloud of strings containing particles in the framework of the Lyra geometry by considering five-dimensional Bianchi type-III line element. We assume two physically plausible conditions (i) shear scalar (σ) proportional to the expansion factor (θ), which leads to P = Qn; n ≠ 0 is a constant, P and Q being scale factors and (ii) ξ = ξ0 = constant, ξ being the coefficient of bulk viscosity, deterministic models of our Universe are obtained. We have solved the modified Einstein’s field equations of a homogeneous Bianchi type-III metric. The bihaviors of cosmographic parameters for the different values of time (t) and redshift (z) are presented in detail to study the proposed model. It has been found that the displacement vector (β) behaves itself like the cosmological term, and the solution is consistent with the recent observations of SNeIa. The physical and geometrical properties of the model are premeditated, and it has been discussed in detail regarding the possibilities and prospects that can be happen throughout the evolution of the Universe. It is found that the bulk viscosity plays a crucial role in the evolution of the Universe, and the strings dominate in the early Universe and eventually disappear from the Universe during a sufficiently large time. So, our model can be treated as a realistic one.