Abstract
We present the relation between the sphaleron energy and the gravitational wave signals from a first order electroweak phase transition. The crucial ingredient is the scaling law between the sphaleron energy at the temperature of the phase transition and that at zero temperature. We estimate the baryon number preservation criterion, and observe that for a sufficiently strong phase transition, it is possible to probe the electroweak sphaleron using measurements of future space-based gravitational wave detectors.
Highlights
The first direct detection of gravitational wave signals from the binary black hole merger by LIGO [1] and the approval of the space-based interferometer LISA [2] have raised growing interest on the study of gravitational waves from a first-order electroweak phase transition (EWPT) in the early universe
We first summarize the relations among the phase transition strength, gravitational waves from the EWPT, and the baryon number preservation criterion (BNPC) here: (1) a higher detectability of the stochastic background of gravitational waves generally requires a smaller β=Hn and a larger α of the EWPT, where the sound waves in the plasma dominates the gravitational wave production, and this corresponds to a higher strength of the EWPT [12,13]
We find that signal-to-noise ratio (SNR) > 10 corresponds to vn=Tn ≥ 3.46 in the xSM along the tendency of the plots [56], and EsphðTnÞ with the largest SNR at LISA is of a typical value ∼1.8 × 4πv=g which is smaller than the sphaleron energy in the standard model
Summary
The first direct detection of gravitational wave signals from the binary black hole merger by LIGO [1] and the approval of the space-based interferometer LISA [2] have raised growing interest on the study of gravitational waves from a first-order electroweak phase transition (EWPT) in the early universe. We first summarize the relations among the phase transition strength, gravitational waves from the EWPT, and the baryon number preservation criterion (BNPC) here: (1) a higher detectability of the stochastic background of gravitational waves generally requires a smaller β=Hn (roughly the inverse time duration of the phase transition) and a larger α (the latent heat normalized by the radiation energy) of the EWPT, where the sound waves in the plasma dominates the gravitational wave production, and this corresponds to a higher strength of the EWPT [12,13] Both parameters are highly related with the finite temperature potential that determines the sphaleron energy (EsphðTÞ) inside the electroweak bubbles. We use the extensively studied singlet extended standard model (“xSM”) and the standard model effective field theory (SMEFT) as two representative examples [29], with the former and the latter driven by tree-level renormalizable and nonrenormalizable operators, respectively [28]
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