If a fraction of the dark matter is unstable and decays into dark radiation at around the time of matter-radiation equality, it could impact the expansion history of the universe in a way that helps to ameliorate the long-standing tension between the locally measured value of the Hubble constant and the value inferred from measurements of the cosmic microwave background and baryon acoustic oscillations (assuming standard $��$CDM cosmology). If this component of decaying dark matter is cold, however, it will modify the evolution of the gravitational potentials, leading to inconsistencies with these same data sets. With this in mind, we consider here a component of decaying warm dark matter, with a free-streaming length that is long enough to remain consistent with existing data. We study the background and perturbation evolution of warm decaying dark matter, and use cosmological data to constrain the mass, abundance and decay rate of such a particle. We find that a component of warm decaying dark matter can significantly reduce the tension between local and cosmological determinations of the Hubble constant.

33 pages, 8 figures. References added; matches published version