On the importance of radiation-era initial conditions for tensor perturbations

TL;DR

We address whether primordial tensor perturbations conserve on super-horizon scales through the radiation era and show that the answer hinges on the initial state of the free-streaming plasma after reheating. Using a stochastic-gravity framework, we derive the tensor equation of motion with an anisotropic stress $\pi_{ij}$ split into explicit and implicit contributions and analyze two free-streaming models (conformally coupled scalars and photons) under local versus global equilibrium initial conditions. The main result is that local (tensor-perturbed) initial conditions yield the standard kinetic-theory conservation, with $\pi_{ij}$ producing only the expected decaying mode, whereas a globally homogeneous initial state yields an effective graviton mass and strong suppression of tensor amplitudes. This reconciles discrepancies in the literature by showing the evolution is extremely sensitive to the reheating initial state, and supports the conventional inflation-to-CMB mapping. The findings reinforce the role of local thermalization in preserving super-horizon tensor perturbations and provide a controlled framework for assessing other plasma models.

Abstract

Conservation of super-horizon tensor fluctuations is crucial for connecting inflation to observations. Starting from first principles, recent works have found violations of this conservation if free-streaming radiation is produced during reheating. We show that the non-conservation is sensitive to the radiation initial state, and argue that the physical state should be affected by tensor perturbations that are already present during reheating. The deviation from super-horizon conservation is then negligible, recovering the standard result from kinetic theory. In contrast, a globally homogeneous and isotropic plasma state leads to a large suppression of tensor amplitudes. This difference between the local (physical) and global thermal equilibrium settles the discrepancy between the older and recent literature.