Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory

Hirvonen, J.; Löfgren, Johan; Ramsey-Musolf, Michael J.; Schicho, Philipp; Tenkanen, Tuomas V. I.

doi:10.1007/jhep07(2022)135

Cited by 27 publications

(23 citation statements)

References 166 publications

(303 reference statements)

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“…These three problems-in addition to gauge dependence [57,60,64]-result in order-ofmagnitude uncertainties for the rate. This is important as these uncertainties propagate to gravitational-wave predictions [17,58].…”

Section: Uncertainties For Thermal Escapementioning

confidence: 99%

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Bubble nucleation to all orders

Ekstedt

2022

J. High Energ. Phys.

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This paper extends classical results by Langer and Kramers [1–3] and combines them with modern methods from high-temperature field theory [4–8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders — the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9–11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4–7, 12–14], all results only hold within this framework.

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Section: Uncertainties For Thermal Escapementioning

confidence: 99%

“…effective theory can be used to both calculate equilibrium quantities and the nucleation rate [46,47,63,64].…”

Section: Jhep08(2022)115mentioning

confidence: 99%

Bubble nucleation to all orders

Ekstedt

2022

J. High Energ. Phys.

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“…However, recent work has described how to extend such a computation to higher orders [64][65][66][67] (also c.f. [68][69][70]). In the work at hand, we will not focus on such an improvement for the bubble nucleation rate, but instead treat T n as an input parameter that we vary; once its computation at higher orders is available, our results for the pressure, sound speed and the kinetic energy fraction can be used to determine the actual effect on GW power spectra.…”

Section: Computation Of the Pressure And Sound Speedmentioning

confidence: 99%

“…In all following plots, we demonstrate the results obtained in the 3d EFT with fixed RG scales 3 . It should be noted that an accurate prediction of the gravitational wave spectrum depends on the nucleation temperature, which enters in H * , R * , f p,0 and K. A self-consistent determination of the nucleation temperature requires a computation of the bubble nucleation rate within the 3d nucleation EFT [65] (for applications, see [64,69]). This goes beyond the scope of this work.…”

Section: Impact On Gravitational Wave Predictionsmentioning

confidence: 99%

“…We emphasise, that compared to [62] in which the SM pressure is computed, we use a different power counting for the 3d Higgs mass parameter. In this reference, in the context of pure SM, the proper counting is µ 2 h,3 ∼ g 3 3 , which corresponds to a radiatively generated barrier (see for a similar discussion the recent work [69,82]), whereas here we use µ 2 h,3 ∼ g 2 3 which corresponds to the case with a tree-level barrier in a two-step phase transition of the Higgs and singlet.…”

Section: A Dimensional Reduction and Pressure With O(n ) Singletmentioning

confidence: 99%

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Speed of sound in cosmological phase transitions and effect on gravitational waves

Tenkanen,

van de Vis

2022

Preprint

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The energy budget for gravitational waves of a cosmological first order phase transitions depends on the speed of sound in the thermal plasma in both phases around the bubble wall. Working in the real-singlet augmented Standard Model, which admits a strong twostep electroweak phase transition, we compute higher order corrections to the pressure and sound speed. We compare our result to lower-order approximations to the sound speed and the energy budget and investigate the impact on the gravitational wave signal. We find that deviations in the speed of sound from c 2 s = 1/3 are enhanced up to O(5%) in our higher-order computation. This results in a suppression in the energy budget of up to O(50%) compared to approximations assuming c 2 s = 1/3. The effect is most significant for hybrid and detonation solutions. We generalise our discussion to the case of multiple inert scalars and the case of a reduced number of fermion families in order to mimic hypothetical dark sector phase transitions. In this sector with modified field content, the sound speed can receive significant suppression, with potential order-of-magnitude impact on the gravitational wave amplitude.

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Perturbative effective field theory expansions for cosmological phase transitions

Gould,

Tenkanen

2024

J. High Energ. Phys.

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Guided by previous non-perturbative lattice simulations of a two-step electroweak phase transition, we reformulate the perturbative analysis of equilibrium thermodynamics for generic cosmological phase transitions in terms of effective field theory (EFT) expansions. Based on thermal scale hierarchies, we argue that the scale of many interesting phase transitions is in-between the soft and ultrasoft energy scales, which have been the focus of studies utilising high-temperature dimensional reduction. The corresponding EFT expansions provide a handle to control the perturbative expansion, and allow us to avoid spurious infrared divergences, imaginary parts, gauge dependence and renormalisation scale dependence that have plagued previous studies. As a direct application, we present a novel approach to two-step electroweak phase transitions, by constructing separate effective descriptions for two consecutive transitions. Our approach provides simple expressions for effective potentials separately in different phases, a numerically inexpensive method to determine thermodynamics, and significantly improves agreement with the non-perturbative lattice simulations.

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Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory

Cited by 27 publications

References 166 publications

Bubble nucleation to all orders

Bubble nucleation to all orders

Speed of sound in cosmological phase transitions and effect on gravitational waves

Perturbative effective field theory expansions for cosmological phase transitions

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