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Theories of modified gravity generically violate the strong equivalenceprinciple, so that the internal dynamics of a self-gravitating system in freefall depends on the strength of the external gravitational field (the externalfield effect). We fit rotation curves (RCs) from the SPARC database with amodel inspired by Milgromian dynamics (MOND), which relates the outer shape ofa RC to the external Newtonian field from the large-scale baryonic matterdistribution through a dimensionless parameter $e_{\rm N}$. We obtain a$>4\sigma$ statistical detection of the external field effect (i.e. $e_{\rmN}>0$ on average), confirming previous results. We then locate the SPARCgalaxies in the cosmic web of the nearby Universe and find a striking contrastin the fitted $e_{\rm N}$ {values} for galaxies in underdense versus overdenseregions. Galaxies in an underdense region between 22 and 45 Mpc from thecelestial axis in the northern sky have RC fits consistent with $e_{\rmN}\simeq0$, while those in overdense regions adjacent to the CfA2 great walland the Perseus-Pisces supercluster return $e_{\rm N}$ that are a factor of twolarger than the median for SPARC galaxies. We also calculate independentestimates of $e_{\rm N}$ from galaxy survey data and find that they agree withthe $e_{\rm N}$ inferred from the RCs within the uncertainties, the chiefuncertainty being the spatial distribution of baryons not contained in galaxiesor clusters.

astrophysical journal/the astrophysical journal

Testing the Strong Equivalence Principle. II. Relating the External  Field Effect in Galaxy Rotation Curves to the Large-Scale Structure of the  Universe