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 ${\varphi }^{(1)},{\varphi }^{(2)}.$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 $M\times \{{\varphi }^{(1)}\}\times \{{\varphi }^{(2)}\}$ with M a FRW space is given.