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

TL;DR

This paper derives Raychaudhuri equations within Finsler-Randers spacetime and generalized scalar-tensor theories, exploring their implications for cosmology and energy conditions in such geometries.

Contribution

It introduces Raychaudhuri equations for Finsler-Randers spaces and a generalized geometrical framework involving scalar fields, extending previous models.

Findings

Derived Raychaudhuri equations for Finsler-Randers spacetime.

Analyzed energy conditions in Finsler cosmology.

Applied equations to a FRW-based model with scalar fields.

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.