Lambda CDM Suitably Embedded in f(R) with a Non-Minimal Coupling to Matter

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, f1 and f2, where the first one generalises the Hilbert-Einstein action, while the second couples to the matter Lagrangian. On the one hand, assuming a Lambda CDM background, we calculate analytical solutions for the functions f1 and f2. We consider two setups: on the first one, we fix f2 and compute f1 and on the second one, we fix f1 and compute f2. 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 f1 and f2. We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe