Numerical simulations of acoustically generated gravitational waves at a first order phase transition

Abstract

We present details of numerical simulations of the gravitational radiation produced by a first order thermal phase transition in the early Universe. We confirm that the dominant source of gravitational waves is sound waves generated by the expanding bubbles of the low-temperature phase. We demonstrate that the sound waves have a power spectrum with a power-law form between the scales set by the average bubble separation (which sets the length scale of the fluid flow L f ) and the bubble wall width. The sound waves generate gravitational waves whose power spectrum also has a power-law form, at a rate proportional to L f and the square of the fluid kinetic energy density. We identify a dimensionless parameterΩ GW characterizing the efficiency of this "acoustic" gravitational wave production whose value is 8πΩ GW ≃ 0.8 AE 0.1 across all our simulations. We compare the acoustic gravitational waves with the standard prediction from the envelope approximation. Not only is the power spectrum steeper (apart from an initial transient) but the gravitational wave energy density is generically larger by the ratio of the Hubble time to the phase transition duration, which can be 2 orders of magnitude or more in a typical first order electroweak phase transition.

Bubble expansion and the viability of singlet-driven electroweak baryogenesis

“…The ingredients presented in this study can be used to more precisely compute the resulting gravity wave spectrum in concrete models involving singlets. Recent work [67,68] suggests that the peak amplitude of the signal from a strong electroweak-scale phase transition may in fact be significantly larger than previously realized. It would be interesting to analyze singlet driven phase transitions given these new hydrodynamic insights along with our predictions for the wall velocity in concrete models.…”

“…refs. [1,4,[55][56][57][58][59][60][61][62][63][64][65][66][67][68]). These scenarios may be effectively probed by upcoming gravitational wave experiments, such as eLISA [69], or Big Bang Observer [70].…”

Gravitational waves from a supercooled electroweak phase transition and their detection with pulsar timing arrays

“…The production of GWs from a first-order phase transition originates from three sources: the collisions of bubbles walls [1][2][3][4][5]36,37], sound waves in the plasma formed after collision [57][58][59][60] and magnetohydrodynamics turbu-lences in the plasma [61][62][63][64][65]. As these three contributions should approximately linearly combine [12], the total energy density can be written…”

Gravitational waves from hidden QCD phase transition

“…where h is the dimensionless Hubble parameter, Ω ϕ stands for the scalar field contribution from collisions of bubble walls [61][62][63][64][65][66], Ω sw for the contribution from sound waves in plasma after the bubble collisions [67][68][69][70], and Ω turb for the contribution from magnetohydrodynamic (MHD) turbulence in plasma [71][72][73][74]. Following [12], each contribution is given for a given set of the parameters (T t , α,β) with the velocity of bubble wall v w and the κ ϕ , κ v , and κ turb which are the fraction of vacuum energy, respectively, converted into gradient energy of scalar field, bulk motion of the fluid, and MHD turbulence.…”