Stochastic inflation as a superfluid
Phys. Rev. D 111, 123523 – Published 13 June, 2025
DOI: https://doi.org/10.1103/l1sp-yzmg
Abstract
We point out that inflationary superhorizon fluctuations can be effectively described by a set of equations analogous to those governing a superfluid. This is achieved through a functional Schrödinger approach to the evolution of the inflationary wave function, combined with a suitable coarse-graining procedure to capture large-scale dynamics. The irrotational fluid velocity is proportional to the gradient of the wave-function phase. Marginalizing over short superhorizon modes introduces an external force acting on the fluid velocity. The quantum pressure characteristic of the superfluid plays a role in scenarios involving an ultra-slow-roll phase of inflation. Our superfluid framework is consistent with the standard Starobinsky approach to stochastic inflation while offering complementary insights, particularly by providing more precise information on the phase of the inflationary wave function. We also discuss a heuristic approach to include dissipative effects in this description.