$$\varLambda $$ Λ CDM suitably embedded in f(R) with a non-minimal coupling to matter

Abstract

Abstract 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, $$f_1$$ f 1 and $$f_2$$ 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 $$\varLambda $$ Λ CDM background, we calculate analytical solutions for the functions $$f_1$$ f 1 and $$f_2$$ f 2 . We consider two setups: on the first one, we fix $$f_2$$ f 2 and compute $$f_1$$ f 1 and on the second one, we fix $$f_1$$ f 1 and compute $$f_2$$ 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 $$f_1$$ f 1 and $$f_2$$ f 2 . We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe.