  By using a novel technique that establishes a correspondence between general
relativity and metric-affine theories based on the Ricci tensor, we are able to
set stringent constraints on the free parameter of Born-Infeld gravity from the
ones recently obtained for Born-Infeld electrodynamics by using light-by-light
scattering data from ATLAS. We also discuss how these gravity theories plus
matter fit within an effective field theory framework.
