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

In this paper, we show that the baryon-to-photon ratio eta is in general not conserved before decoupling in nonminimally coupled theories of gravity. We use big-bang nucleosynthesis and cosmic microwave background (CMB) limits on the baryon-to-photon ratio eta to derive new constraints on modified gravity theories with a universal nonminimal 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.