Tilted congruences with stiff fluid cosmological models
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ORIGINAL PAPER
Tilted congruences with stiff fluid cosmological models V J Dagwal1,2*
and D D Pawar1,2
1
Department of Mathematics, Government College of Engineering, Nagpur 441 108, India
2
School of Mathematical Sciences, Swami Ramanand Teerth, Marathwada University, Vishnupuri Nanded 431 606, India Received: 16 January 2019 / Accepted: 03 September 2019
Abstract: We have presented tilted Bianchi type-VI0 cosmological models in general theory of relativity. To solve ~ considering time varying radial velocity x ¼ T a and uniform Einstein’s field equation, we have used the stiff fluid p~r ¼ q, radial velocity x ¼ x0 , where a; x0 are constant. We have also investigated the behaviors of some physical parameters. Keywords: Bianchi type-VI0; Tilted models; Stiff fluid PACS No.: 04.50.kd
1. Introduction The studies of these models are usually distinguished between two different scenarios: when the fluid congruence is normal to the hyper surfaces of homogeneity and when it is not. The models of the first kind are called orthogonal or non-tilted, and of the second kind are called tilted models. In a tilted Bianchi cosmology, the tilt can become extreme in a finite time as measured along the fluid congruence, with the result that the group orbits become time-like. This means that the models are no longer spatially homogeneous. There has been a considerable interest in investigating spatially homogeneous and anisotropic cosmological models in which matter does not move orthogonal to the hyper surface of homogeneity. Such types of models are called tilted cosmological models. A spatially homogeneous cosmology is said to be tilted if the fluid velocity vector is not orthogonal to the group orbits, otherwise the model is said to be non-tilted. The tilted models are more complicated than those of non-tilted one. In tilted model, the fluid flow lines are no longer orthogonal to the surfaces of homogeneity, thus the four-velocity ui is not parallel to the normal vector ni . At this point, in addition to the fluid pressure and density, we have the peculiar velocity of the fluid relative to the normal vectors. In spatially homogeneous model, we have the major
*Corresponding author, E-mail: [email protected]
models of theoretical cosmology because they express the idea of the cosmological principle: All the points of space at the same time are equivalent to each other. The differences between tilted and co-moving models are, in co-moving model it gives zero value to the threevelocity of any fluid element i.e. vanishing three velocity and in tilted (non-co-moving) model, the three-velocity represents additional degree of freedom and tilted model have detected the presence of dissipative processes included gravitational radiation. The different aspects of tilted cosmological models have been examined by King and Ellis [1], Ellis and King [2], Collins and Ellis [3], Coley and Hervik [4]. The stability of non-tilted Bianchi models against tilt was obtained by Barrow and Hervik [5]. Nilsson et al. [6] have investigated non-til
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