Gravitational wave spectra from strongly supercooled phase transitions
Marek Lewicki, Ville Vaskonen
Abstract
Abstract We study gravitational wave (GW) production in strongly supercooled cosmological phase transitions, taking particular care of models featuring a complex scalar field with a U(1) symmetric potential. We perform lattice simulations of two-bubble collisions to properly model the scalar field gradients, and compute the GW spectrum sourced by them using the thin-wall approximation in many-bubble simulations. We find that in the U(1) symmetric case the low-frequency spectrum is $$\propto \omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∝</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> whereas for a real scalar field it is $$\propto \omega ^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>ω</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> </mml:math> . In both cases the spectrum decays as $$\omega ^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> at high frequencies.