  For most of cosmic history, the evolution of our Universe has been governed
by the physics of a 'dark sector', consisting of dark matter and dark energy,
whose properties are only understood in a schematic way. The influence of these
constituents is mediated exclusively by the force of gravity, meaning that
insight into their nature must be gleaned from gravitational phenomena. The
advent of gravitational-wave astronomy has revolutionised the field of black
hole astrophysics, and opens a new window of discovery for cosmological
sources. Relevant examples include topological defects, such as domain walls or
cosmic strings, which are remnants of a phase transition. Here we present the
first simulations of cosmic structure formation in which the dynamics of the
dark sector introduces domain walls as a source of stochastic gravitational
waves in the late Universe. We study in detail how the spectrum of
gravitational waves is affected by the properties of the model, and extrapolate
the results to scales relevant to the recent evidence for a stochastic
gravitational wave background. Our relativistic implementation of the field
dynamics paves the way for optimal use of the next generation of gravitational
experiments to unravel the dark sector.
