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Since 2015 the gravitational-wave observations of LIGO and Virgo havetransformed our understanding of compact-object binaries. In the years to come,ground-based gravitational-wave observatories such as LIGO, Virgo, and theirsuccessors will increase in sensitivity, discovering thousands of stellar-massbinaries. In the 2030s, the space-based LISA will provide gravitational-waveobservations of massive black holes binaries. Between the $\sim10$-$10^3~\mathrm{Hz}$ band of ground-based observatories and the$\sim10^{-4}$-$10^{-1}~\mathrm{Hz}$ band of LISA lies the uncharted decihertzgravitational-wave band. We propose a Decihertz Observatory to study thisfrequency 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 detectstellar-mass binaries days to years before they merge, providing early warningof nearby binary neutron star mergers and measurements of the eccentricity ofbinary black holes, and they will enable new tests of general relativity andthe Standard Model of particle physics. Here we summarise how a DecihertzObservatory could provide unique insights into how black holes form and evolveacross cosmic time, improve prospects for both multimessenger astronomy andmultiband gravitational-wave astronomy, and enable new probes of gravity,particle physics and cosmology.

The missing link in gravitational-wave astronomy: A summary of discoveries waiting in the decihertz range