  We study 1-loop corrections to the primordial stochastic background of
gravitational waves produced during inflation. While in single-clock, at the
leading order in slow-roll, quantum corrections keep the amplitude scale-free
this is not the case when the pattern of symmetry breaking is different. In
particular, when spatial diffeomorphisms are also broken during inflation as
for solid inflation, a log-running in the external momentum is generated. We
relate the appearance of a log-running to the spontaneous breaking of
dilatation invariance. The running could be instrumental to distinguish
single-clock from alternative models of inflation in future high sensitivity
CMB polarisation and GWs experiments.
