Cosmology from non-minimal geometry-matter coupling

Abstract

We construct a cosmological model from the inception of the Friedmann-Lem\^aitre-Robertson-Walker metric into the field equations of the \(f(R,L_m)\) gravity theory, with \(R\) being the Ricci scalar and \(L_m\) being the matter lagrangian density. The formalism is developed for a particular \(f(R,L_m)\) function, namely \(R/16\pi +(1+\sigma R)L_{m}\), with \(\sigma\) being a constant that carries the geometry-matter coupling. Our solutions are remarkably capable of evading the Big-Bang singularity as well as predict the cosmic acceleration with no need for the cosmological constant, but simply as a consequence of the geometry-matter coupling terms in the Friedmann-like equations.