Cosmology from non-minimal geometry-matter coupling

We construct a cosmological model from the inception of the Friedmann-Lemâitre-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. (© 2023 Wiley‐VCH GmbH.)