On Bianchi Type Cosmological Models in Lyra’s Geometry

EYL [1] first try to unify gravitation and electromagnetism in single space-time geometry. He showed how one can introduce vector field in the Riemannian space time with an intrinsic geometric significance, but this theory was not accepted. Later Lyra’s [2] proposed a modification of Riemannian geometry by introducing a gauge function into the structureless manifold that bears close resemblance to Weyl’s geometry and removes non integrability condition arises in Weyl’s geometry. In this way Riemannian geometry was given a new modification by Lyra’s geometry Sen [3] found that the static with finite density in Lyra’s modified Riemannian geometry is similar to the static Einstein model. Sen and Dunn [4] proposed a new scalar tensor theory of gravitation and constructed the field equations analogous to the Einstein’s field equations based on the Lyra’s Geometry. Halford [5] has pointed out that the constant vector displacement field i  in Lyra’s Geometry plays the role of cosmological constant in the normal general relativistic treatment. Further, it was shown by Halford that the scalar tensor treatment based on Lyra’s Geometry predicts the same effects, within the observational limit, as in Einstein theory. Several researchers have studied cosmological models based on Lyra’s geometry with a constant displacement field. Beesham [6] considered FRW models with a time dependent field. Singh and Singh [7] have presented Bianchi type I, II and Kantowaski-Sachs cosmological models with a time dependent displacement field and have made a comparative study of the Robertson-Walker Models with a constant deceleration parameter in Einstein’s theory with cosmological term and in the cosmological theory based on Lyra’s geometry. The essential difference between the cosmological theories based on Lyra’s geometry and Riemannian geometry