Revisiting the envelope approximation: gravitational waves from bubble collisions

Understand

We study the envelope approximation and its applicability to first-order phase transitions in the early universe.

• We demonstrate that the power laws seen in previous studies exist independently of the nucleation rate.
• We also compare the envelope approximation prediction to results from large-scale phase transition simulations.
• For phase transitions where the contribution to gravitational waves from scalar fields dominates over that from the coupled plasma of light particles, the envelope approximation is in agreement, giving a power spectrum of the same form and order of magnitude.