A direct detection of primordial gravitational waves is the ultimate probe for any inflation model. While current CMB bounds predict the generic scale-invariant spectrum to be below the reach of upcoming gravitational wave interferometers, this prospect may dramatically change if the inflaton is a pseudoscalar. In this case, a coupling to an abelian gauge field leads to a tachyonic instability for the latter and hence to a new source of gravitational waves, directly related to the dynamics of inflation. In this talk I discuss how this setup enables the upcoming gravitational wave interferometers advanced LIGO/VIRGO and eLISA to probe the microphysics of inflation, distinguishing between different universality classes of single-field slow-roll inflation models. We find that the prime candidates for an early detection is a Starobinsky-like model.