On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal (1809.08242v2)

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 $f \gtrsim 10^{-4}$ 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.

• The paper demonstrates that supercooling can intensify phase transition strength while imposing strict bubble percolation constraints.
• The paper employs a comprehensive numerical framework covering nucleation, growth, and percolation to accurately model gravitational wave amplitudes.
• The paper shows that gravitational wave signals are realistically predicted at frequencies above 10⁻⁴ Hz, aligning detection prospects with space-based observatories like LISA.

An Examination of the Strength of Electroweak Phase Transitions and Associated Gravitational Wave Signals

The paper authored by Ellis, Lewicki, and No presents an in-depth analysis of the upper limits on the strength of first-order electroweak phase transitions in the context of scenarios beyond the Standard Model (BSM), focusing specifically on the implications for gravitational wave (GW) signals. The central question addressed is how significant supercooling during such a phase transition influences both the transition itself and the resultant GW spectrum, particularly when the vacuum energy becomes the dominant factor in the Universe's expansion.

The authors explore the potential and constraints of electroweak phase transitions induced by models with polynomial potentials, like extensions featuring a dimension-6 operator or the inclusion of a real singlet scalar field. Through comprehensive numerical analysis, they demonstrate that while supercooling can indeed elevate the transition strength, it imposes stringent limits on successful bubble percolation, thus constraining the maximum feasible transition strength. The critical insight is that if the transition is delayed until the vacuum energy begins to shape cosmic expansion, percolation may fail—a re-emergence of the "graceful-exit" dilemma from inflationary cosmology.

In their analysis, the authors deploy a systematic framework accounting for nucleation, growth, and percolation of phase transition bubbles. This enhanced treatment reveals that prevailing estimations of GW amplitudes, predominantly from sound waves, may significantly overestimate the actual signals when supercooling is pronounced. Instead, the authors illuminate how turbulence could play a more influential role in the late stages of phase transitions.

Key numerical findings of the paper indicate that despite theoretical predictions of strong phase transitions peaking at low GW frequencies, observational constraints necessitate these transitions to occur at characteristic frequencies above around $10^{-4}$ Hz. This is crucial as it means such signals are predominantly detectable by space-based detectors like LISA rather than ground-based detectors or pulsar timing arrays.

Theoretical and experimental implications are substantial. In practice, this research proposes robust constraints and models that assist in pinpointing parameters that would yield detectable GW signals from past electroweak phase transitions, potentially observable by next-generation observatories. Theoretically, the dialogue around phase transitions in cosmology is enriched by these insights, especially in reconciling supercooling with a complete transition and aligning GW literature predictions with physical observability limits.

Furthermore, the exploration of conformal models hints at scenarios where significant deviations could occur — prompting future investigations into these unique cases where the nature of scalar potentials might allow for more robust predictions regarding bubble collisions and their GW signatures.

In conclusion, the work by Ellis, Lewicki, and No advances our understanding of electroweak phase transitions and their cosmic imprints via gravitational waves, laying the groundwork for both theoretical innovation and empirical inquiry in the field of particle cosmology. As the hunt for such signals intensifies with upcoming observational missions, this paper provides a valuable reference point for interpreting results within a controlled theoretical framework.