  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.
