Stochastic inflation as a superfluid

TL;DR

This paper introduces a novel superfluid analogy for inflationary superhorizon fluctuations, using a quantum wavefunction approach to better understand large-scale inflation dynamics and phase information.

Contribution

It develops a superfluid framework for inflationary fluctuations via a functional Schrödinger approach, enhancing the understanding of phase and quantum effects in inflation.

Findings

Superfluid analogy captures inflationary superhorizon fluctuations.

Quantum pressure influences ultra-slow-roll inflation scenarios.

Framework aligns with and extends stochastic inflation models.

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 Schr\"odinger approach to the evolution of the inflationary wavefunction, combined with a suitable coarse-graining procedure to capture large-scale dynamics. The irrotational fluid velocity is proportional to the gradient of the wavefunction 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 wavefunction. We also discuss a heuristic approach to include dissipative effects in this description.