Gravitational wave energy budget in strongly supercooled phase transitions (1903.09642v3)

Abstract: We derive efficiency factors for the production of gravitational waves through bubble collisions and plasma-related sources in strong phase transitions, and find the conditions under which the bubble collisions can contribute significantly to the signal. We use lattice simulations to clarify the dependence of the colliding bubbles on their initial state. We illustrate our findings in two examples, the Standard Model with an extra $|H|^6$ interaction and a classically scale-invariant $U(1){\rm B-L}$ extension of the Standard Model. The contribution to the GW spectrum from bubble collisions is found to be negligible in the $|H|^6$ model, whereas it can play an important role in parts of the parameter space in the scale-invariant $U(1){\rm B-L}$ model. In both cases the sound-wave period is much shorter than a Hubble time, suggesting a significant amplification of the turbulence-sourced signal. We find, however, that the peak of the plasma-sourced spectrum is still produced by sound waves with the slower-falling turbulence contribution becoming important off-peak.

• The paper reveals that bubble collisions are negligible in a modified Standard Model but can be significant in a conformally invariant U(1)₍B-L₎ model.
• It utilizes lattice simulations to compute efficiency factors for gravitational wave generation from both bubble collisions and plasma sources.
• The study emphasizes that the combined contributions of sound waves and turbulence are key to predicting observable gravitational wave signals.

Overview of "Gravitational wave energy budget in strongly supercooled phase transitions"

The paper "Gravitational wave energy budget in strongly supercooled phase transitions," authored by John Ellis, Marek Lewicki, Ville Vaskonen, and Jose Miguel No, explores the production of gravitational waves (GWs) in the context of strongly supercooled first-order phase transitions. The paper primarily focuses on efficiency factors for the generation of GWs resulting from both bubble collisions and plasma-related sources within such transitions. The authors employ lattice simulations to investigate the implications of initial bubble states in these transitions.

Efficient GW Production from Phase Transitions

The analysis identifies conditions under which bubble collisions can significantly contribute to the GW signal. Two illustrative examples are provided to demonstrate the findings: a modified Standard Model (SM) incorporating a non-renormalizable $|H|^6$ interaction and a classically scale-invariant $U(1)_{\rm B-L}$ extension of the Standard Model. It is found that in the modified SM, the contribution from bubble collisions to the GW spectrum is negligible. In contrast, the $U(1)_{\rm B-L}$ model can exhibit cases where bubble collisions play a significant role.

Theoretical and Practical Implications

The paper reveals that, irrespective of the model, the sound-wave period is notably shorter than a Hubble time, implying a more substantial impact from turbulence-sourced signals post-transition. However, the peak contribution to the GW spectrum, even when dominated by plasma sources, originates from sound waves, with a more slowly declining turbulent contribution becoming increasingly relevant off-peak.

Results and Model Investigations

• Modified Standard Model with $|H|^6$ Interaction: The research confirms that significant supercooling does not occur, which aligns with prior findings, rendering bubble collision signals negligible. The energy is predominantly consumed in plasma motion rather than wall acceleration.
• Conformally Invariant $U(1)_{\rm B-L}$ Model: Here, strong supercooling is feasible, potentially producing notable GW signals from bubble collisions. Further exploration of bubble collisions versus plasma GW sources is discussed.

Numerical Simulations and Energy Budget

Lattice simulations elucidate the dynamics of bubble growth in supercooled transitions. The derived expressions for efficiency factors contribute to precise predictions of relative source strengths. A noteworthy observation is the oscillatory behavior of fields around potential minima post-transition, influencing the expansion rate and validation of GW signals during matter-like evolution phases in some parameter spaces.

Future Developments and Conclusions

The research suggests that scenarios allowing for significant supercooling, like the classically scale-invariant model, could potentially be observed in future GW experiments, given the prospect of observable GW signals from bubble collisions. The delineation of efficiency factors offers a crucial tool for probing early Universe physics via GW detection, enhancing our understanding of phase transition dynamics in different theoretical models.

Future developments in GW detectors will benefit from this paper's comprehensive model predictions, particularly those sensitive to the sub-Hz range, like LISA, DECIGO, and BBO, which could provide empirical confirmation of theoretical predictions discussed in the paper. Advances in simulation techniques will continue to refine the predictions made here, possibly revealing new avenues for research into cosmological phase transitions and their observable signatures.