Any new vector boson with non-zero mass (a 'dark photon' or 'Proca boson') that is present during inflation is automatically produced at this time from vacuum fluctuations and can comprise all or a substantial fraction of the observed dark matter density, as shown by Graham, Mardon, and Rajendran. We demonstrate, utilising both analytic and numerical studies, that such a scenario implies an extremely rich dark matter substructure arising purely from the interplay of gravitational interactions and quantum effects. Due to a remarkable parametric coincidence between the size of the primordial density perturbations and the scale at which quantum pressure is relevant, a substantial fraction of the dark matter inevitably collapses into gravitationally bound solitons, which are fully quantum coherent objects. The central densities of these 'dark photon star', or 'Proca star', solitons are typically a factor 10(6) larger than the local background dark matter density, and they have characteristic masses of 10(-16) M-circle dot (10(-5) eV/m)(3/2), where m is the mass of the vector. During and post soliton production a comparable fraction of the energy density is initially stored in, and subsequently radiated from, long-lived quasi-normal modes. Furthermore, the solitons are surrounded by characteristic 'fuzzy' dark matter halos in which quantum wave-like properties are also enhanced relative to the usual virialized dark matter expectations. Lower density compact halos, with masses a factor of similar to 10(5) greater than the solitons, form at much larger scales. We argue that, at minimum, the solitons are likely to survive to the present day without being tidally disrupted. This rich substructure, which we anticipate also arises from other dark photon dark matter production mechanisms, opens up a wide range of new direct and indirect detection possibilities, as we discuss in a companion paper.
