General SIGW source for reheating dynamics

TL;DR

The paper provides a gauge-invariant, second-order formulation for scalar-induced gravitational waves (SIGW) during a general reheating era, allowing a smooth transition from inflation to radiation or matter-dominated phases. By treating an inflaton field plus fluids and keeping four scalar metric degrees of freedom, the authors derive an effective tensor equation that couples the gravitational-wave perturbation to curvature perturbations and anisotropic stress, while ensuring gauge invariance up to second order. The central result is a gauge-independent evolution equation for the tensor mode $\boldsymbol{\vartheta}^{\text{t}}_{ij}$ with a source term built from quadratic combinations of curvature perturbations $\mathcal{R}_{\varphi}$ and $\mathcal{R}_{nv}$, plus the tensor anisotropic stress $\Pi^{\text{t}}_{ij}$, and a counterterm $\mathcal{Q}^{\text{t}}_{ij}$ to remove residual gauge artifacts. This framework enables robust predictions of SIGW signals across reheating dynamics and offers pathways to study scenarios like warm inflation with hydrodynamic fluctuations, where short-distance noise is mitigated by the tensor counterterm.”

Abstract

Working in an arbitrary gauge, we derive the source term for scalar-induced gravitational waves (SIGW) valid during a general reheating epoch. Specifically, the dominant energy component is allowed to transition smoothly from an inflaton field to a radiation fluid, possibly via a period of matter domination. Gauge invariance is verified up to second order.