Gravitational waves from colliding vacuum bubbles in gauge theories
Marek Lewicki, Ville Vaskonen
Abstract
Abstract We study production of gravitational waves (GWs) in strongly supercooled cosmological phase transitions in gauge theories. We extract from two-bubble lattice simulations the scaling of the GW source, and use it in many-bubble simulations in the thin-wall limit to estimate the resulting GW spectrum. We find that in presence of the gauge field the GW source decays with bubble radius as $$\propto R^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> after collisions. This leads to a GW spectrum that follows $$\Omega _{\mathrm{GW}} \propto \omega ^{2.3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>GW</mml:mi> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mn>2.3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at low frequencies and $$\Omega _{\mathrm{GW}} \propto \omega ^{-2.9}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>GW</mml:mi> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2.9</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at high frequencies, marking a significant deviation from the popular envelope approximation.