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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The search for the existence of Lyra manifold in a hybrid universe interacting with Van der Waals fluid using Bianchi type III metric is presented in this paper. To find the exact cosmological solutions, we use certain physical relations between the metric potentials and the average scale factor is assumed to be [Formula: see text] (see Ref. 1) describing the hybrid character of scale factor with the generation of a model of transitioning phase from early decelerating to the present accelerating universe. In this model, when we investigate further about the role of the Van der Waals fluid with Lyra geometry, interestingly, we found that this universe behaves as one containing with dark energy and at the late stage a part of the dark energy behaves as phantom type. This part being generated by the Lyra manifold itself may be taken as a source of dark energy. Some physical as well as geometrical aspects of the model universe are also presented.

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Here, we have investigated the interaction of Bianchi type-I anisotropic cloud string cosmological model universe with electromagnetic field in the context of general relativity. In this paper, the energy-momentum tensor is assumed to be the sum of the rest energy density and string tension density with an electromagnetic field. To obtain exact solution of Einstein’s field equations, we take the average scale factor as an integrating function of time. Also, the dynamics and significance of various physical parameters of model are discussed.