Gravitational waves from bubble dynamics: beyond the envelope

Abstract

We study gravitational-wave production from bubble dynamics (bubble collisions and sound waves) during a cosmic first-order phase transition with an analytic approach. We first propose modeling the system with the thin-wall approximation but without the envelope approximation often adopted in the literature, in order to take bubble propagation after collisions into account. The bubble walls in our setup are considered as modeling the scalar field configuration and/or the bulk motion of the fluid. We next write down analytic expressions for the gravitational-wave spectrum, and evaluate them with numerical methods. It is found that, in the long-lasting limit of the collided bubble walls, the spectrum grows from ∝ f 3 to ∝ f 1 in low frequencies, showing a significant enhancement compared to the one with the envelope approximation. It is also found that the spectrum saturates in the same limit, indicating a decrease in the correlation of the energy-momentum tensor at late times. We also discuss the implications of our results to gravitational-wave production both from bubble collisions (scalar dynamics) and sound waves (fluid dynamics).

Relativistic bubble collisions—a closer look

“…The false vacuum trapping has a huge impact on the resulting GW spectrum, since it leads to a decelerating pressure on the propagating scalar field and therefore changes the extent of energy penetration after collision [39]. Ultimately, the 'trapping equation' determines which mechanism of GW production prevails after the phase transition: The so-called envelope approximation [5,6,35,36] or the bulk flow model [37,38]. Figure 24: How the right panel of Fig.…”

“…These mean that, after the energy peaks propagate over a distance much longer than the bubble radius at collisions, their distance is much shorter than the radius of the bubble-like structures. Therefore, the IR structure pointed out in Ref [37]. may appear in the GW spectrum.…”

Di-Higgs production in the 4b channel and gravitational wave complementarity

“…The GW spectra can be obtained by plugging these parameters into a set of analytical formulae, obtained by fitting to results from numerical simulations of different GW production mechanisms. It has been realized in recent years [41] that the dominant contribution comes from sound waves, although significant advances have also been made in both analytical modeling and numerical simulations of pure bubble collision contributions [42][43][44][45]. By evolving the scalar-field and fluid model on a 3-dimensional lattice, the gravitational wave energy density spectrum can be extracted [36]:…”

A more attractive scheme for radion stabilization and supercooled phase transition

“…where Ω col h 2 , Ω sw h 2 and Ω turb h 2 denote the contributions from bubble collisions [59][60][61][62][63][64], sound wave [65][66][67][68], and turbulence [69][70][71][72][73][74] of the thermal plasma, respectively. In the absence of the thermal plasma, most of the released energy is converted into the kinetic energy of the accelerating bubble wall, and hence, the bubble wall velocity before collisions is very close to the speed of light.…”