Quantum Field Theory Of Cosmological Perturbations Induced By Ultralight Dark Matter

Abstract

The growth of primordial perturbations during the matter-dominated era is primarily driven by dark matter. Ultralight scalar fields (ULDM) are a promising candidate for this role, conventionally modeled as operating in a classical, high-occupation regime. In this work, we develop a first-principles field-theoretic framework to investigate the impact of ULDM on linear cosmological perturbations during matter domination, explicitly retaining its quantum nature. Deriving a closed equation for the graviton field dynamics, we compute and regularize its source terms for a generic Gaussian initial state of the ULDM field within the adiabatic (WKB) approximation, employing the middle-point working assumption for non-local terms. After gauge-fixing we find that, contrary to previous claims, the classical condensate of ULDM has no influence on gravitational wave propagation. However, the time-dependent graviton effective mass induced by quantum pressure of the squeezed state can drive parametric resonance in specific primordial gravitational wave modes. We demonstrate this growth is negligible for non-relativistic ULDM at matter-radiation equality under the assumption of a power-law squeezing spectrum for masses in the range $m \sim 10^{-21}{-}10^{-24}$ eV.