  Atom interferometers (AIs) as gravitational-wave (GW) detectors have been
proposed a decade ago. Both ground and space-based projects will be in
construction and preparation in the near future. In this paper, for the first
time, we investigate the potential of the space-borne AIs on detecting GW
standard sirens and hence the applications on cosmology. We consider AEDGE as
our fiducial AI GW detector and estimate the number of bright sirens that would
be obtained within a 5-years data-taking period of GW and with the follow-up
observation of electromagnetic (EM) counterparts. We then construct the mock
catalogue of bright sirens and predict their ability on constraining
cosmological parameters such as the Hubble constant, dynamics of dark energy,
and modified gravity theory. Our preliminary results show around order
$\mathcal{O} (30)$ bright sirens can be obtained from a 5-years operation time
of AEDGE and the follow-up observation of EM counterparts. The bright sirens
alone can measure $H_0$ with a precision of 2.1\%, which is sufficient to
arbitrate the Hubble tension. Combining current most precise electromagnetic
experiments, the inclusion of AEDGE bright sirens can improve the measurement
of the equation of state of dark energy, though marginally. Moreover, by
modifying GW propagation on cosmological scales, the deviations from general
relativity (modified gravity theory effects) can be constrained at 5.7\%
precision level.
