We study the envelope approximation and its applicability to first-orderphase transitions in the early universe. We demonstrate that the power lawsseen in previous studies exist independently of the nucleation rate. We alsocompare the envelope approximation prediction to results from large-scale phasetransition simulations. For phase transitions where the contribution togravitational waves from scalar fields dominates over that from the coupledplasma of light particles, the envelope approximation is in agreement, giving apower spectrum of the same form and order of magnitude. In all other cases theform and amplitude of the gravitational wave power spectrum is markedlydifferent and new techniques are required.
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