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In this work, we obtain the Raychaudhuri equations for various types ofFinsler spaces as the Finsler-Randers (FR) space-time and in a more generalgeometrical structure of the space-time manifold which contains two fibres thatare two scalars which represent inflaton fields $\phi^{(1)}, \phi^{(2)}.$Inaddition, the energy-conditions are studied in a FR cosmology and arecorrelated with FRW model. Finally an application of Raychaudhuri equation forthe model $M \times \{ \phi^{(1)} \} \times \{ \phi^{(2)} \}$ with M a FRWspace is given.

Raychaudhuri equation in the Finsler-Randers spacetime and Generalized scalar-tensor theories