  We discuss a cosmological phase transition within the Standard Model which
incorporates spontaneously broken scale invariance as a low-energy theory. In
addition to the Standard Model fields, the minimal model involves a light
dilaton, which acquires a large vacuum expectation value (VEV) through the
mechanism of dimensional transmutation. Under the assumption of the
cancellation of the vacuum energy, the dilaton develops a very small mass at
2-loop order. As a result, a flat direction is present in the classical
dilaton-Higgs potential at zero temperature while the quantum potential admits
two (almost) degenerate local minima with unbroken and broken eletroweak
symmetry. We found that the cosmological electroweak phase transition in this
model can only be triggered by a QCD chiral symmetry breaking phase transition
at low temperatures, $T\lesssim 132$ MeV. Furthermore, unlike the standard
case, the universe settles into the chiral symmetry breaking vacuum via a
first-order phase transition which gives rise to a stochastic gravitational
background with a peak frequency $\sim 10^{-8}$ Hz as well as triggers the
production of approximately solar mass primordial black holes. The observation
of these signatures of cosmological phase transitions together with the
detection of a light dilaton would provide a strong hint of the fundamental
role of scale invariance in particle physics.
