New limits on warm inflation from pulsar timing arrays

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 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.