  In this paper, we investigate scalar-induced gravitational waves (GWs)
generated in the post-inflationary universe to infer new limits on warm
inflation. We specifically examine the evolution of primordial GWs produced by
scalar perturbations produced during the radiation-dominated epoch. For this
purpose, we assume a weak regime of warm inflation under the slow-roll
approximation, with a dissipation coefficient linearly dependent on the
temperature of the radiation bath. We then derive analytical expressions for
the curvature power spectrum and the scalar index, in the cases of chaotic and
exponential potentials of the inflationary field. Subsequently, we compare the
theoretical predictions regarding the relic energy density of GWs with the
stochastic GW background signal recently detected by the NANOGrav collaboration
through the use of pulsar timing array measurements. In so doing, we obtain
numerical constraints on the free parameters of the inflationary models under
study. Finally, we conduct a model selection analysis through the Bayesian
inference method to measure the statistical performance of the different
theoretical scenarios.
