Real-time Gravitational Wave Response in Thermal Spinning fields

TL;DR

This paper investigates how the spin content of thermal plasmas influences gravitational wave propagation in a radiation-dominated universe, finding that spin-dependent effects cancel out, leaving a universal long-term response.

Contribution

It introduces a real-time quantum-field-theoretic framework to analyze spin effects on gravitational waves in thermal fields, revealing the cancellation of spin-dependent responses.

Findings

Spin-dependent responses occur on short time scales.

Local responses cancel the dynamical spin effects.

The long-term gravitational wave response is universal.

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.