Numerical simulations of acoustically generated gravitational waves at a first order phase transition (1504.03291v2)

Abstract: We present details of numerical simulations of the gravitational radiation produced by a first order thermal phase transition in the early universe. We confirm that the dominant source of gravitational waves is sound waves generated by the expanding bubbles of the low-temperature phase. We demonstrate that the sound waves have a power spectrum with a power-law form between the scales set by the average bubble separation (which sets the length scale of the fluid flow $L_\text{f}$) and the bubble wall width. The sound waves generate gravitational waves whose power spectrum also has a power-law form, at a rate proportional to $L_\text{f}$ and the square of the fluid kinetic energy density. We identify a dimensionless parameter $\tilde\Omega_\text{GW}$ characterising the efficiency of this "acoustic" gravitational wave production whose value is $8\pi\tilde\Omega_\text{GW} \simeq 0.8 \pm 0.1$ across all our simulations. We compare the acoustic gravitational waves with the standard prediction from the envelope approximation. Not only is the power spectrum steeper (apart from an initial transient) but the gravitational wave energy density is generically larger by the ratio of the Hubble time to the phase transition duration, which can be 2 orders of magnitude or more in a typical first order electroweak phase transition.

• The paper shows that sound waves dominate gravitational wave production over bubble wall collisions by employing large-scale numerical simulations.
• The study finds that gravitational wave spectra exhibit a steep power-law, challenging the traditional envelope approximation.
• Results indicate that fluid velocity and bubble scale critically influence gravitational wave amplitudes, informing future detection strategies.

Numerical Simulations of Acoustically Generated Gravitational Waves at a First Order Phase Transition

This paper presents a detailed paper of the generation of gravitational waves (GWs) during cosmological first-order phase transitions, specifically focusing on the mechanism of acoustic production through sound waves. The researchers utilize large-scale numerical simulations to explore how expanding bubbles in the early universe generate fluid motions that subsequently produce gravitational waves.

Overview and Methodology

The authors investigate the scenario where a first-order thermal phase transition in the early universe, analogous to that at the electroweak scale, could give rise to gravitational wave signals observable today. The paper is motivated by the enhanced detection capabilities anticipated with future space-based interferometers like eLISA, making it timely yet broadly applicable to ongoing and future theoretical and experimental GW astrophysics.

Numerical simulations are deployed to model the interaction between a scalar field—the order parameter of the transition—and an ideal fluid that represents the cosmic plasma. The gravitational wave production primarily stems from sound waves in the fluid rather than the kinetic energy on the scalar bubble walls. This approach is distinctly different from the traditional envelope approximation method, which assumes energy concentration on thin bubble walls and significantly underestimates the amplitude of generated gravitational waves.

The numerical model is informed by previous studies on bubble dynamics in vacuum transitions, now extended to thermal transitions involving fluid interactions. This adaptation considers energy exchange between the scalar field and the fluid, capturing the hydrodynamics more accurately, especially as it pertains to subsonic deflagrations and supersonic detonations.

Key Findings

1. Dominance of Acoustic GW Production: The simulations demonstrate that sound waves resulting from the fluid dynamics are the dominant source of gravitational radiation during the transition. This is characterized by a dimensionless parameter, $GW$, which accounts for the efficiency of gravitational wave production from sound waves, indicating an enhancement over predictions made using the envelope approximation.
2. Power-law Spectra: The gravitational wave spectra produced exhibit a power-law behavior, with the results showing steeper UV tails than the $k^{-1}$ prediction from the envelope approximation. For weak deflagrations, a $k^{-3}$ power law emerges, aligning more closely with the dynamics involved in sound wave production.
3. Impact of Bubble Scale and Flow Lifetime: The gravitational wave density parameter is found to be proportional to the fourth power of the fluid velocity and the product of the source flow lifetime and the characteristic scale (average bubble separation). These parameters are shown to differ substantially from those used in traditional models, suggesting that acoustic mechanisms should be preferred in relevant astrophysical analyses.

Practical and Theoretical Implications

The outcome of this research suggests a paradigm shift in how gravitational wave generation is modeled in the context of cosmological phase transitions. The underestimation by the envelope approximation, when compared to the proposed acoustic mechanism, can be rectified by considering the longer-lasting sound wave effects extending beyond the active phase transition.

Additionally, this work implies that gravitational wave observations of a primordial source could potentially reveal details about the early universe dynamics, such as the nature of the phase transition and properties of the cosmic fluid at that time. The authors contend that the methodologies and insights here can be broadly applied to future analyses of gravitational wave signals, whether they emerge from thermal phase transitions at the electroweak scale or beyond.

Future Directions

Further exploration could focus on varying the degree of supercooling and phase transition strengths to broaden the applicability of the findings to other cosmological events. Moreover, incorporating higher-resolution simulations and extending the studied parameter space may clarify the behavior of fluid motions at scales closer to real-world transitions.

These developments have the potential to refine theoretical predictions and interpretations of future gravitational wave detections, paving the way for new understanding in cosmology. The sound-wave-centric model proposed here offers a presumably more accurate framework for predicting GW signals from first-order phase transitions in the early universe, underscoring its importance for both theoretical paper and experimental verification.