The paper deals with the investigation of a homogeneous and anisotropic space-time described by Bianchi type III metric with perfect fluid in Lyra geometry setting. Exact solutions of the Einsten's field equations have been obtained under the assumption of quadratic equation of state (EoS) of the form p = aρ 2 − ρ , where a is a constant and strictly a > 0. The physical and geometrical aspects are also examined in details. AbstractThe paper deals with the investigation of a homogeneous and anisotropic space-time described by Bianchi type III metric with perfect fluid in Lyra geometry setting. Exact solutions of the Einsten's field equations have been obtained under the assumption of quadratic equation of state (EoS) of the form p = aρ 2 − ρ , where a is a constant and strictly a > 0. The physical and geometrical aspects are also examined in details.

In the course of investigation of our present universe by considering the five-dimensional locally rotationally symmetric (LRS) Bianchi type-I universe with timedependent deceleration parameters in Lyra manifold, it is excitingly found that the geometry itself of Lyra manifold behaves and consistent with present observational findings for accelerating universe. The behavior of the universes and their contribution to the process of evolution are examined. While studying their physical, dynamical and kinematical properties for different cases, it is found that this model is a new and viable form of model universe containing dark energy. It will be very helpful in explaining the present accelerated expansion behavior of the universe.

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Considering five dimensional plane symmetric metric, we discuss a model universe with different situations, by solving the modified Einstein field equations within the framework of Lyra geometry. We obtain many interesting realistic solutions governing the present day model of the universe. Physical and kinematical properties of the models are discussed in detail.

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