  We present an updated analysis of the first-order phase transition associated
with symmetry breaking in the early Universe in a classically scale-invariant
model extended with a new SU(2) gauge group. Including recent developments in
understanding supercooled phase transitions, we compute all of its
characteristics and significantly constrain the parameter space. We then
predict gravitational wave spectra generated during this phase transition and
by computing the signal-to-noise ratio we conclude that this model is well
testable (and falsifiable) with LISA. We also provide predictions for the relic
dark matter abundance. It is consistent with observations in a rather narrow
part of the parameter space, since we exclude the so-called supercool dark
matter scenario based on an improved description of percolation and reheating
after the phase transition as well as inclusion of the running of couplings.
Finally, we devote attention to renormalisation-scale dependence of the
results. Even though our main results are obtained with the use of
renormalisation-group improved effective potential, we also perform a
fixed-scale analysis which proves that the dependence on the scale is not only
qualitative but also quantitative.
