An extended theory of gravity in a modified Riemann’s geometry

Abstract

In this work, we study the evolution of an isotropic universe in an extended theory of gravity obtained geometrically by transforming the normal-gauge Lyra displacement vector field [Formula: see text] as a complex vectorial function depending on a dynamical scalar field [Formula: see text]. By using the latest observational data, we observe that for [Formula: see text] the universe starts accelerating at the critical scale factor [Formula: see text] which corresponds to a redshift of [Formula: see text]. We also find that the dark energy fluid considered in this model is a generalized fluid with equation of state [Formula: see text].