  The double copy is a much-studied relationship between scattering amplitudes
in gauge and gravity theories, that has subsequently been extended to classical
field solutions. In nearly all previous examples, the graviton field is defined
around Minkowski space. Recently, it has been suggested that one may set up a
double copy for gravitons defined around a non-trivial background. We
investigate this idea from the point of view of the classical double copy.
First, we use Kerr-Schild spacetimes to construct graviton solutions in curved
space, as double copies of gauge fields on non-zero gauge backgrounds. Next, we
find that we can reinterpret such cases in terms of a graviton on a
non-Minkowski background, whose single copy is a gauge field in the same
background spacetime. The latter type of double copy persists even when the
background is not of Kerr-Schild form, and we provide examples involving
conformally flat metrics. Our results will be useful in extending the remit of
the double copy, including to possible cosmological applications.
