Inflationary Kicks and Coulomb Filtering of Spectator Dark Matter
Light spectator fields provide a compelling inflationary origin for scalar dark matter, but their primordial fluctuations often generate excessive isocurvature perturbations on large scales. We develop a novel, exactly solvable filtering mechanism based on a tower of $δ-$function contributions to the spectator mass, which we call kicks, whose dense limit converges to a smooth Coulomb-like profile. The filter produces a isocurvature spectrum during inflation that is strongly suppressed on large scales, rises with momenta as $k^3$ in the infrared, and, after a rapid turnover, smoothly approaches a constant plateau at small scales. This construction is motivated by a discrete translational invariance, admits an EFT regime in which radiative corrections can be systematically controlled, and can find a concrete realization in terms of an inflationary massive-clock model. We embed the filter in a minimal dark-matter scenario in which a spectator condensate oscillates about the minimum of a quadratic potential and behaves as pressureless matter. In this framework, the spectator dark-matter mass is directly related to the turnover scale of the inflationary isocurvature spectrum. We determine the resulting dark-matter abundance and analyze the relevant isocurvature and backreaction constraints. The most restrictive realization, in which the spectator condensate is generated during inflation, favors a relatively low inflationary scale.