Searching for new physics with pulsar timing arrays: the case of induced gravitational waves and primordial black holes

Recent pulsar timing array (PTA) datasets provide substantial evidence for the existence of a stochastic gravitational wave background in the nano-Hz frequency range. While the leading mechanism to explain such a signature relies on supermassive black hole mergers, it is also possible that a cosmological SGWB contributes to the observed signal. In this talk, we will discuss in details the case of gravitational waves induced at second order in the early universe, a scenario which is accompanied by the formation of a sizeable abundance of primordial black holes. We will review some recent progress on the characterization of such a signal and discuss the potential constraints PTA observations could set on this scenario, as well as on the inflationary dynamics underlying these models.