Shape of the acoustic gravitational wave power spectrum from a first order phase transition (1704.05871v3)

Abstract: We present results from large-scale numerical simulations of a first order thermal phase transition in the early universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted $k^{-3}$ behaviour, where $k$ is the wavenumber, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-$k$ decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wavenumber behaviour of the velocity power spectrum is consistent with a causal $k^{3}$, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about $0.05c$, produced from bubbles with a mean separation of about $10^{-2}$ of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

• The paper demonstrates that numerical simulations reveal distinct power-law behaviors in the acoustic gravitational wave spectrum from first-order phase transitions.
• It identifies critical length scales, such as the mean bubble separation and sound shell thickness, that determine the spectral peak and dynamics.
• The research quantifies parameters suggesting that LISA could detect these gravitational waves, particularly in transitions featuring fluid velocities around 0.05c.

Insights from Numerical Simulations of Acoustic Gravitational Waves from First-Order Phase Transitions

In the paper titled "Shape of the acoustic gravitational wave power spectrum from a first-order phase transition," the authors Mark Hindmarsh, Stephan J. Huber, Kari Rummukainen, and David J. Weir present a comprehensive analysis of gravitational waves generated by first-order phase transitions in the early universe. Through extensive numerical simulations, this research examines the shapes of acoustic gravitational wave and velocity power spectra, providing crucial insights into the potential detectability of these signals with space-based experiments like LISA (Laser Interferometer Space Antenna).

Summary of Methods and Results

The authors conduct large-scale numerical simulations based on a model where a scalar field undergoes a first-order phase transition, interacting with a relativistic fluid through frictional dynamics that dissipate the energy from the scalar field into the fluid. They consider two primary scenarios: deflagrations and detonations, characterized by the speed at which bubble walls move through the early universe's plasma.

Key results include the observation of a distinct $k^{-3}$ behavior in the gravitational wave power spectrum for detonations, aligning with predictions from the sound shell model. This model describes how sound waves, generated during the bubble collisions in a phase transition, emit gravitational radiation. For deflagrations, the power spectra exhibit a steeper high-wavenumber decay, introducing additional features not entirely accounted for by the current model.

Their simulations reveal two important length scales: the mean bubble separation and the thickness of the sound shell around expanding bubbles in the low-temperature phase, with the latter determining the peak position of the power spectrum. Moreover, they provide simulation-based parameters for a broken power law fitting formula, facilitating predictions for gravitational wave signals well-removed from the speed of sound.

Implications and Future Work

The paper has significant implications for understanding gravitational waves as cosmic messengers. The authors demonstrate that a LISA-like mission could potentially detect these signals, particularly sensitive to transitions with mean bubble separations around $10^{-2}$ of the Hubble radius and root-mean-square fluid velocities around $0.05c$. Precisely measuring these gravitational waves could offer estimates for the bubble wall speeds and constraints on parameters governing early-universe phase transitions.

This research propels theoretical developments by providing a more accurate and nuanced understanding of gravitational wave production mechanisms during cosmological phase transitions, emphasizing the significance of the relationship between the wall speed, the sound shell thickness, and the resulting power spectrum. These insights could potentially inform the development of new models and simulation techniques to address discrepancies and improve interpretations of gravitational wave signatures.

Future investigations may benefit from exploring the transition to turbulence in the fluid flow, especially in scenarios where shock formation becomes relevant. Further numerical simulations could assist in refining the model and aligning it more closely with observational prospects from forthcoming experimental missions such as ESA’s LISA.

Conclusion

The analysis presented in this paper makes meaningful progress in characterizing gravitational waves emanating from early-universe phase transitions. It refines predictions for future observational missions, addressing how these cosmic signals can reveal conditions of the early universe. These contributions are pivotal for advancing our understanding of the universe’s thermal history and for probing new physics beyond the Standard Model through gravitational wave astronomy.