Eddington-inspired Born-Infeld gravity: Constraints from the generalized parton distributions (GPDs)

Abstract

The Eddington-inspired Born-Infeld (EiBI) theory of gravity modifies general relativity in high-density regimes. It offers an alternative framework that avoids cosmological singularities and remodels gravitational dynamics within compact objects. An important feature of EiBI gravity is its additional parameter, $\kappa$, which governs deviations from standard gravitational behavior. In this study, we investigate constraints on $\kappa$ using the internal pressure distribution of the proton, derived from gravitational form factor (GFF) $ D(t) $ obtained through a QCD analysis of generalized parton distributions (GPDs). By comparing pressure profiles extracted from skewness-dependent GPDs with previous determinations based on deeply virtual Compton scattering (DVCS) data, we establish updated bounds on $\kappa$. Our results show that the choice of proton pressure model significantly impacts the constraints, with the strongest limits ($|\kappa| \leq 0.10\text{--}0.3\, \text{m}^5\, \text{kg}^{-1}\, \text{s}^{-2}$). We further demonstrate that constraints obtained based on the first and second moments of the pressure distribution yield competitive bounds compared to those derived from peak pressures or those derived from just the first moment. These findings highlight the importance of precise experimental and theoretical determinations of the proton's mechanical properties in testing alternative theories of gravity. The present study motivates future improvements in GPD reconstructions for stronger constraints on EiBI gravity and related modifications.