  Gravitational waves produced from the merger of binary neutron stars (BNSs)
are accompanied by electromagnetic counterparts, making it possible to identify
the associated host galaxy. We explore how properties of the host galaxies
relate to the astrophysical processes leading to the mergers. It is thought
that the BNS merger rate within a galaxy at a given epoch depends primarily on
the galaxy's star-formation history as well as the underlying merger time-delay
distribution of the binary systems. The stellar history of a galaxy, meanwhile,
depends on the cosmological evolution of the galaxy through time, and is tied
to the growth of structure in the Universe. We study the hosts of BNS mergers
in the context of structure formation by populating the Universe Machine
simulations with gravitational-wave events~ according to a simple time-delay
model. We find that different time-delay distributions predict different
properties of the associated host galaxies, including the distributions of
stellar mass, star-formation rate, halo mass, and local and large-scale
clustering of hosts. BNSs that merge today with short delay times prefer to be
in hosts that have high star-formation rates, while those with long delay times
live in dense regions within massive halos that have low star formation. We
show that with ${\mathcal O}(10)$ events from current gravitational-wave
detector networks, it is possible to make preliminary distinctions between
formation channels which trace stellar mass, halo mass, or star-formation rate.
We also find that strategies to follow up gravitational-wave events with
electromagnetic telescopes can be significantly optimized using the clustering
properties of their hosts.
