The fate of primordial gravitational waves during domain-wall domination

Abstract

Primordial gravitational waves probe inflation, but their interpretation depends on their subsequent evolution. During domain-wall domination, a frozen wall network retains a nonzero shear response that can modify the superhorizon evolution of primordial gravitational waves. Starting from the wall-forming scalar field, we derive an effective tensor mass term and a source associated with the frozen wall geometry in the thin-wall, quasistatic limit. Together they drive superhorizon tensor perturbations toward a configuration set by the network. This configuration carries both any inherited primordial deformation and the network's intrinsic random structure. We derive how these contributions enter the tensor transfer and power spectrum. The resulting description connects superhorizon tensor evolution to the microscopic wall response and the geometry established as the network freezes.