Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories (2007.08537v3)

Abstract: We undertake a careful analysis of stochastic gravitational wave production from cosmological phase transitions in an expanding universe, studying both a standard radiation as well as a matter dominated history. We analyze in detail the dynamics of the phase transition, including the false vacuum fraction, bubble lifetime distribution, bubble number density, mean bubble separation, etc., for an expanding universe. We also study the full set of differential equations governing the evolution of plasma and the scalar field during the phase transition and generalize results obtained in Minkowski spacetime. In particular, we generalize the sound shell model to the expanding universe and determine the velocity field power spectrum. This ultimately provides an accurate calculation of the gravitational wave spectrum seen today for the dominant source of sound waves. For the amplitude of the gravitational wave spectrum visible today, we find a suppression factor arising from the finite lifetime of the sound waves and compare with the commonly used result in the literature, which corresponds to the asymptotic value of our suppression factor. We point out that the asymptotic value is only applicable for a very long lifetime of the sound waves, which is highly unlikely due to the onset of shocks, turbulence and other damping processes. We also point out that features of the gravitational wave spectral form may hold the tantalizing possibility of distinguishing between different expansion histories using phase transitions.

• The paper determines the quantitative properties of bubble nucleation and its impact on gravitational wave production in both radiation- and matter-dominated universes.
• It computes the gravitational wave power spectrum via the sound shell model and reveals a suppression factor (Υ) that adjusts the amplitude of the signals.
• The study implies that incorporating non-linear effects like shocks and turbulence in simulations is crucial for future gravitational wave detection with instruments such as LISA.

Analysis of Stochastic Gravitational Waves from Cosmological Phase Transitions

The paper "Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories" by Guo et al. explores the theoretical framework and quantitative analysis of stochastic gravitational waves generated by cosmological first-order phase transitions. The authors focus their paper on scenarios within both standard radiation-dominated and non-standard matter-dominated cosmological histories, providing detailed insights into the dynamics of this mechanism in an expanding universe.

The paper begins by examining the bubble nucleation rate, a vital component of the phase transition dynamics. Through rigorous calculations, the authors derive expressions for the nucleation rate in both expanding and non-expanding universes, accounting for variables such as bubble lifetime distribution and mean bubble separation. These measures are critical as they form the basis for understanding the timing and distribution of nucleation events which subsequently influence gravitational wave production.

The paper then expands into calculating the gravitational wave power spectrum, emphasizing the contribution of sound waves arising from the rapid expansion and collision of bubbles. The authors adopt the sound shell model, which enables computation of the gravitational wave spectra with high precision by modeling the fluid dynamics associated with this process. They carefully address the expansion effects on these dynamics by comparing Minkowski spacetime results to those within various cosmological backgrounds, finding that simple rescalings allow for straightforward generalization of existing models.

Key results presented within the paper include:

• The determination that the velocity profile within the sound shell model remains consistent between Minkowski and FLRW spacetimes. This finding simplifies the transition from standard theoretical analyses to more complex cosmological models.
• The identification of a suppression factor, $\Upsilon$, which modifies the amplitude of gravitational wave signals under various conditions. The authors highlight that existing literature largely assumes the asymptotic limit of $\Upsilon=1$, a simplification that overlooks potential damping effects from turbulence and other non-linear processes.

The paper also speculates on the practical implications of these findings. Particularly, it anticipates advancements in gravitational wave detection capabilities—via instruments such as LISA—that could further establish these theoretical predictions. Moreover, the potential differentiation of expansion histories based on gravitational wave spectral forms could elucidate the nature of early universe conditions, notably in scenarios deviating from radiation-dominated paradigms.

Looking toward the future, the authors suggest that refining simulations and incorporating non-linearities such as shocks and turbulence will be essential in furthering our understanding of phase transition-induced gravitational waves. Additionally, exploring realistic treatment of entropy injections in matter-dominated histories could provide insights into hidden sectors and beyond-the-standard-model physics.

Overall, this paper represents a comprehensive analysis of gravitational wave generation from cosmological phase transitions, offering significant contributions to theoretical astrophysics and cosmology. By extending existing models to accommodate the complexities of an expanding universe, the authors provide a robust framework for research at the intersection of particle physics, cosmology, and astronomy.