Free Streaming in Warm Wave Dark Matter

Abstract: We provide a framework for numerically computing the effects of free-streaming in scalar fields produced after inflation. First, we provide a detailed prescription for setting up initial conditions in the field. This prescription allows us to specify the power spectra of the fields (peaked on subhorizon length scales and without a homogeneous field mode), and importantly, also correctly reproduces the behaviour of density perturbations on large length scales consistent with superhorizon adiabatic perturbations. We then evolve the fields using a spatially inhomogeneous Klein-Gordon equation, including the effects of expansion and radiation-sourced metric perturbations. We show how gravity enhances, and how free streaming erases the initially adiabatic density perturbations of the field, revealing more of the underlying, non-evolving, white-noise isocurvature density contrast. Furthermore, we explore the effect of non-gravitational self-interactions of the field, including oscillon formation, on the suppression dynamics. As part of this paper, we make our code, ${\sf{Cosmic-Fields-Lite}}$ (${\sf{CFL}}$), publicly available. For observationally accessible signatures, our work is particularly relevant for structure formation in light/ultralight dark matter fields.