LAUSR

In this work, we further study a metric modified theory of gravity which contains a non-minimal coupling to matter, more precisely, we assume two functions of the scalar curvature, $$f_1$$ and $$f_2$$ , where the first one generalises the Hilbert–Einstein action, while the second couples to the matter Lagrangian. On the one hand, assuming a $$\varLambda $$ CDM background, we calculate analytical solutions for the functions $$f_1$$ and $$f_2$$ . We consider two setups: on the first one, we fix $$f_2$$ and compute $$f_1$$ and on the second one, we fix $$f_1$$ and compute $$f_2$$ . Moreover, we do the analysis for two different energy density contents, a matter dominated universe and a general perfect fluid with a constant equation of state fuelling the universe expansion. On the other hand, we complete our study by performing a cosmographic analysis for $$f_1$$ and $$f_2$$ . We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe.