Stochastic gravitational waves present an observational challenge and an opportunity for discovering new physics in the early universe. Several mechanisms can produce stochastic gravitational waves, albeit with different characteristics. I will describe (if time permits) three different scenarios of GW production.
The first is based on the fragmentation of the inflaton after the end of inflation and the formation of localized long-lived structures called oscillons. Different types of potentials lead to features in the GW spectrum, providing a first tool —at least in principle— of probing the inflationary potential around the origin.
A second scenario is an extension of hybrid inflation with the introduction of an abelian gauge field coupled to the inflaton and waterfall fields. During the waterfall transition, the gauge field gets tachyonically amplified, leading to observable GWs from preheating, for proper parameter choices.
Finally, I will discuss a simpler scenario, where spectator fields roll during the radiation dominated era, and produce fluctuations and subsequent GWs through self-resonance or parametric resonance of a second field. The signal can be detectable in GW observatories, including LISA, and is accompanied by extra relativistic degrees of freedom at the level of sensitivity of next generation CMB experiments.