  We reanalyze the detection possibilities for gravitational waves arising from
cosmological first order phase transitions. We discuss the stochastic
gravitational wave background corresponding to the three expected scenarios of
phase transition dynamics. We then perform an analysis on the detection
possibilities for each case using sensitivities for the next generation
ground-based detector Cosmic Explorer and the current LISA proposal, using two
analysis methods. We find that having both detectors allows wide detection
possibilities over much of the parameter space, including that corresponding to
several points relevant to different early Universe models.
