  We address the issue of black hole scalarization and its compatibility with
cosmic inflation and big bang cosmology from an effective field theory (EFT)
point of view. In practice, using a well-defined and healthy toy model which
(in part) has been broadly considered in the literature, we consider how
higher-order theories of gravity, up to cubic operators in Riemann curvature,
fit within this context. Interestingly enough, we find that already at this
minimal level, there is a non-trivial interplay between the Wilson coefficients
which are otherwise completely independent, constraining the parameter space
where scalarization may actually occur. Conclusively, we claim that the EFT
does exhibit black hole scalarization, remaining compatible with the
inflationary paradigm, and admitting General Relativity as a cosmological
attractor.
