  Flavor violating axion couplings can be in action before recombination, and
they can fill the early universe with an additional radiation component.
Working within a model-independent framework, we consider an effective field
theory for the axion field and quantify axion production. Current cosmological
data exclude already a fraction of the available parameter space, and the
bounds will improve significantly with future CMB-S4 surveys. Remarkably, we
find that future cosmological bounds will be comparable or even stronger than
the ones obtained in our terrestrial laboratories.
