  Since 2015 the gravitational-wave observations of LIGO and Virgo have
transformed our understanding of compact-object binaries. In the years to come,
ground-based gravitational-wave observatories such as LIGO, Virgo, and their
successors will increase in sensitivity, discovering thousands of stellar-mass
binaries. In the 2030s, the space-based LISA will provide gravitational-wave
observations of massive black holes binaries. Between the $\sim
10$-$10^3~\mathrm{Hz}$ band of ground-based observatories and the
$\sim10^{-4}$-$10^{-1}~\mathrm{Hz}$ band of LISA lies the uncharted decihertz
gravitational-wave band. We propose a Decihertz Observatory to study this
frequency range, and to complement observations made by other detectors.
Decihertz observatories are well suited to observation of intermediate-mass
($\sim10^2$-$10^4 M_\odot$) black holes; they will be able to detect
stellar-mass binaries days to years before they merge, providing early warning
of nearby binary neutron star mergers and measurements of the eccentricity of
binary black holes, and they will enable new tests of general relativity and
the Standard Model of particle physics. Here we summarise how a Decihertz
Observatory could provide unique insights into how black holes form and evolve
across cosmic time, improve prospects for both multimessenger astronomy and
multiband gravitational-wave astronomy, and enable new probes of gravity,
particle physics and cosmology.
