If there was a first order phase transition in the early universe, there
should be an associated stochastic background of gravitational waves. In this
paper, we point out that the characteristic frequency of the spectrum due to
phase transitions which took place in the temperature range 100 GeV - 10^7 GeV
is precisely in the window that will be probed by the second generation of
space-based interferometers such as the Big Bang Observer (BBO). Taking into
account the astrophysical foreground, we determine the type of phase
transitions which could be detected either at LISA, LIGO or BBO, in terms of
the amount of supercooling and the duration of the phase transition that are
needed. Those two quantities can be calculated for any given effective scalar
potential describing the phase transition. In particular, the new models of
electroweak symmetry breaking which have been proposed in the last few years
typically have a different Higgs potential from the Standard Model. They could
lead to a gravitational wave signature in the milli-Hertz frequency, which is
precisely the peak sensitivity of LISA. We also show that the signal coming
from phase transitions taking place at T ~ 1-100 TeV could entirely screen the
relic gravitational wave signal expected from standard inflationary models.Comment: 18 pages, 24 figure
