Abstract. In the present study the anisotropic spatially homogeneous Bianchi type-I (B-I) cosmological models in normal gauge for Lyra's manifold has been studied.A deterministic solution by considering the time dependent deceleration parameter which gives average scale factor a(t) = [sinh(αt)]^1/n has been obtained. Einstein's modified field equations for the homogeneous Binachi Type I metric are solved. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.

Full-text: PDF