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

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