Cosmology from Non-Minimal Geometry-Matter Coupling

We construct a cosmological model from the inception of the Friedmann-Lemaitre-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/16p + (1 + sR)L-m, with s 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.