One of the main targets for upcoming gravitational wave observatories is the detection of a primordial stochastic gravitational wave background (SGWB). Such a signal has the potential to shed light on part of the cosmological history not accessible by other means as well as to probe new physics at energy scales beyond the reach of terrestrial experiments.
In this context, I will show how phenomena arising during unconstrained stages of inflation, and motivated by high energy embeddings, lead to characteristic oscillatory patterns in the SGWB.
I will then discuss theoretical threats of these scenarios such as backreaction and perturbative unitarity as well as the current effort
to assess the detection prospects of such features in the SGWB with the upcoming Laser Interferometer Space Antenna (LISA).