Real-time Gravitational Wave Response in Thermal Spinning fields

TL;DR

The paper investigates whether the spin content of thermal radiation alters the real-time gravitational-wave response in a radiation-dominated universe. Using a real-time in-in quantum-field-theory framework, it decomposes the stress tensor into a background, a dynamical (history-dependent) part, and local contact terms, with an on-shell projection fixed by the Friedmann equations. Across spin-0, spin-1/2, and spin-1 fields (conformal scalar, Weyl fermion, and Maxwell), it identifies a short-time, spin-dependent dynamical response that is exactly canceled by the local (on-shell and contact) contributions, leaving a universal, nonlocal slow response in agreement with kinetic theory in the hard thermal limit. The result confirms that the large-scale gravitational-wave dynamics in this cosmological setting is spin-independent, providing a robust bridge between quantum field theory and kinetic descriptions and offering a framework for extensions to nonthermal or non-equilibrium environments.

Abstract

We study how the spin content of the thermal plasmas affects the propagation of gravitational waves in a radiation-dominated universe. As a simple but representative setup, we consider conformal scalar, Weyl fermion, and Maxwell fields that provide the background radiation, and we ask whether the resulting damping and phase shift of gravitational waves retain any memory of their spins. We revisit this question in a real-time quantum-field-theoretic framework, where the stress tensor splits into a background part, a dynamical (history-dependent) response, and local contact terms, with an additional on-shell projection fixed by the Friedmann equation. We find that the dynamical spin-dependent response arises on a short time scale characterized by the radiation temperature, which is exactly canceled by the local responses. As a result, the remaining long-time response is universal and consistent with kinetic theory in the hard thermal limit. Although the underlying mechanism exhibits strong spin dependence, it leaves no observable imprint on the large-scale effective dynamics of gravitational waves in this setup.