Big-bang nucleosynthesis and cosmic microwave background constraints on non-minimally coupled theories of gravity

In this paper we show that the baryon-to-photon ratio $\eta$ is in general not conserved before decoupling in non-minimally coupled theories of gravity. We use big-bang nucleosynthesis and cosmic microwave background limits on the baryon-to-photon ratio $\eta$ to derive new constraints on modified gravity theories with a universal non-minimal coupling between matter and curvature, showing that they rule out a specific class of models previously considered in the literature as a substitute for the dark matter. We also compare these new constraints with the ones obtained from the COBE-FIRAS limits on CMB spectral distortions, highlighting the complementarity between them.