Gravitational Wave Background from Vacuum and Thermal Fluctuations During Axion-Like Inflation

We revisit the framework of axion-like inflation in view of the possibility that the coupling of the inflaton to a non-Abelian topological charge density could lead to the generation of a rapidly thermalizing heat bath. Both dispersive (mass) and absorptive (fric-tion) effects are included. For phenomenologically viable parameters, the system remains in a weak regime of warm inflation (thermal friction << Hubble rate). For tensor perturbations we derive an interpolating formula that incorporates both vacuum and thermal production. The latter yields a model-independent frequency shape similar to f03 in the LISA window, whose co-efficient allows to measure the maximal shear viscosity of the thermal epoch. It is a challenge, however, to find models where the coefficient is large enough to be observable.