  Quantum scale invariance in the UV has been recently advocated as an
attractive way of solving the gauge hierarchy problem arising in the Standard
Model. We explore the cosmological signatures at the electroweak scale when the
breaking of scale invariance originates from a hidden sector and is mediated to
the Standard Model by gauge interactions (Gauge Mediation). These scenarios,
while being hard to distinguish from the Standard Model at LHC, can give rise
to a strong electroweak phase transition leading to the generation of a large
stochastic gravitational wave background in possible reach of future
space-based detectors such as eLISA and BBO. This relic would be the
cosmological imprint of the breaking of scale invariance in Nature.
