  The strong equivalence principle is violated by gravity theories of
Milgromian dynamics (MOND) through the action of the external field effect. We
test two different Lagrangian theories AQUAL and QUMOND based on their
numerical solutions of the external field effect, by comparing two independent
estimates of the mean external field strength of the nearby universe: a
theory-deduced value from fitting the outer rotation curves of 114 galaxies and
an empirical value from the large-scale distribution of cosmic baryons. The
AQUAL-deduced external field strength from rotation curves agrees with that
from the large-scale cosmic environment, while QUMOND-deduced value is somewhat
higher. This suggests that AQUAL is likely to be preferred over QUMOND as an
effective non-relativistic limit of a potential relativistic modified gravity
theory.
