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We formulate a version of the double copy for classical fields in curvedspacetimes. We provide a correspondence between perturbative solutions to thebi-adjoint scalar equations and those of the Yang-Mills equations in positionspace. At the linear level, we show that there exists a map between thesesolutions for maximally symmetric spacetime backgrounds, that provides everyYang-Mills solution by the action of an appropriate differential operator on abi-adjoint scalar solution. Given the existence of a linearized map, we showthat it is possible to cast the solutions of the Yang-Mills equations atarbitrary perturbation order in terms of the corresponding bi-adjoint scalarsolutions. This all-order map is reminiscent of the flat space BCJ double copy,and works for any curved spacetime where the perturbative expansion holds. Weshow that these results have the right flat space limit, and that thecorrespondence is agnostic to the choice of gauge.

The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar