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Recently, a measurement of the pressure distribution experienced by thequarks inside the proton has found a strong repulsive (positive) pressure atdistances up to 0.6 femtometers from its center and a (negative) confiningpressure at larger distances. In this paper we show that this measurement putssignificant constraints on modified theories of gravity in which the strengthof the gravitational interaction on microscopic scales is enhanced with respectto general relativity. We consider the particular case of Eddington-inspiredBorn-Infeld gravity, showing that strong limits on $\kappa$, the onlyadditional parameter of the theory with respect to general relativity, may bederived from the quark pressure measurement ($|\kappa| \lsim 10^{-1} \, {\rmm^5 \, kg^{-1} \, s^{-2}}$). Furthermore, we show how these limits may besignificantly improved with precise measurements of the first and secondmoments of the pressure distribution inside the proton.

Probing gravity at sub-femtometer scales through the pressure distribution inside the proton