On the maximal strength of a first-order electroweak phase transition and its gravitational wave signal

Abstract

What is the maximum possible strength of a first-order electroweak phase transition and the resulting gravitational wave (GW) signal? While naively one might expect that supercooling could increase the strength of the transition to very high values, for strong supercooling the Universe is no longer radiation-dominated and the vacuum energy of the unstable minimum of the potential dominates the expansion, which can jeopardize the successful completion of the phase transition. After providing a general treatment for the nucleation, growth and percolation of broken phase bubbles during a first-order phase transition that encompasses the case of significant supercooling, we study the conditions for successful bubble percolation and completion of the electroweak phase transition in theories beyond the Standard Model featuring polynominal potentials. For such theories, these conditions set a lower bound on the temperature of the transition. Since the plasma cannot be significantly diluted, the resulting GW signal originates mostly from sound waves and turbulence in the plasma, rather than bubble collisions. We find the peak frequency of the GW signal from the phase transition to be generically f 10 −4 Hz. We also study the condition for GW production by sound waves to be long-lasting (GW source active for approximately a Hubble time), showing it is generally not fulfilled in concrete scenarios. Because of this the sound wave GW signal could be weakened, with turbulence setting in earlier, resulting in a smaller overall GW signal as compared to current literature predictions.

Singlet-doublet fermionic dark matter and gravitational waves in a two-Higgs-doublet extension of the Standard Model

“…VI B, the sound wave contribution to the total GW intensity depends on the suppression factor HR * /Ū f depending on whether it lasts more than a Hubble time or not. We estimate the suppression factor HR * /Ū f following [85,146,147] and found it to be < 1 for all the BPs. Due to this fact, following [85,146,147], we include the suppression factor HR * /Ū f to the sound wave component of the GW intensity.…”

“…We estimate the suppression factor HR * /Ū f following [85,146,147] and found it to be < 1 for all the BPs. Due to this fact, following [85,146,147], we include the suppression factor HR * /Ū f to the sound wave component of the GW intensity. In Figure 10 we have plotted and compared the GW intensities for the chosen benchmarks (Table V) DECIGO, aLIGO, aLIGO+ and LISA following Ref.…”

“…To check the contribution of sound wave component to the total GW intensity we need to estimate the suppression factor HR * /Ū f , whereŪ f denotes the root-mean-square (RMS) fluid velocity and R * denotes the mean bubble separation [85,146,147]. If the calculated suppression factor HR * /Ū f of a given model comes out to be > 1 , then the sound wave lasts more than a Hubble time, otherwise it is an overestimate to the GW signal.…”

Gravitational waves from phase transition in minimal SUSY U(1)B−L model

“…When α θ (T ) > 1, vacuum energy stored in the meta-stable vacuum causes inflation of metastable-vacuum region, which hinders the percolation of absolute-vacuum bubbles [29] (first considered for zero-temperature, quantum phase transitions in [30]). In this subsection, we focus on the benchmark of (λ, g B−L , Y M 3 ) = (0.01, 0.4, 1), which has given α θ (T n ) = 1.5, the largest α θ (T n ) among the benchmarks of Section 3.1, and show that the percolation is completed despite large vacuum energy of the meta-stable vacuum.…”

“…(43). A criterion for the completion of the percolation is that [29,33] there is a temperature T p at which I(T p ) = 0.34 and the physical volume of meta-stable-vacuum region decreases with time, i.e.,…”