Cosmological Models of Universe with Variable Deceleration Parameter in Lyra's Manifold

FRW models of the universe have been studied in the cosmological theory based on Lyra’s manifold. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter from which three models of the universe are derived (i) exponential (ii) polynomial and (iii) sinusoidal form respectively. The behaviour of these models of the universe are also discussed. Finally some possibilities of further problems and their investigations have been pointed out.