With the advent of gravitational-wave astronomy it has now been possible to
constrain modified theories of gravity that were invoked to explain the dark
energy. In a class of dilaton models, distances to cosmic sources inferred from
electromagnetic and gravitational wave observations would differ due to the
presence of a friction term. In such theories, the ratio of the Newton's
constant to the fine structure constant varies with time. In this paper we
explore the degree to which it will be possible to test such models. If
collocated sources (e.g. supernovae and binary neutron star mergers), but not
necessarily multimessengers, can be identified by electromagnetic telescopes
and gravitational-wave detectors one can probe if light and gravitational
radiation are subject to the same laws of propagation over cosmological
distances. This helps in constraining the variation of Newton's constant
relative to fine-structure constant. The next generation of gravitational wave
detectors, such as the Cosmic Explorer and Einstein Telescope, in tandem with
the Vera Rubin Observatory and gamma ray observatories such as the Fermi Space
Observatory will be able to detect or constrain such variations at the level of
a few parts in 100. We apply this method to GW170817 with distances inferred by
the LIGO and Virgo detectors and the observed Kilonova