Three different Bianchi type-I cosmological models as related to perfect fluid, with quintessence and with Chaplygin gas, in bimetric theory of gravitation have been deduced. The perfect fluid model has hyperbolic geometry and all its physical parameters are also hyperbolic in nature and therefore they have been studied from hyperbolic geometric view point. All these models are isotropize and shear-less. Other geometrical and physical behaviors of the models have also been studied. The hyperbolic geometric view point of the models will be helpful to the people who use observational data to search for such type of geometry.

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