Causality considerations imply that cosmological fields produced in the early universe can naturally be both warm and noisy, possessing significant gradient and kinetic energy on small scales. I will discuss how these small-scale fluctuations manifest themselves in cosmological and astrophysical observables through free-streaming suppression, scale-dependent enhancement of density fluctuations, and novel nonlinear phenomena such as copious soliton formation. These effects can in turn be used to place bounds on the microscopic properties and production mechanisms of otherwise dark fields. Depending on audience interest, I will also sketch a broadly applicable framework based on field correlators, together with comparisons to fully nonlinear 3+1 dimensional numerical simulations.