Abstract
We demonstrate that the relic gravitational wave background from a multi-step phase transition may deviate from the simple sum of the single spectra, for phase transitions with similar nucleation temperatures TN. We demonstrate that the temperature range ΔT between the volume fractions f(T) = 0.1 and f(T) = 0.9 occupied by the vacuum bubbles can span ∼ 20 GeV. This allows for a situation in which phase transitions overlap, such that the later bubbles may nucleate both in high temperature and intermediate temperature phases. Such scenarios may lead to more exotic gravitational wave spectra, which cannot be fitted that of a consecutive PTs. We demonstrate this explicitly in the singlet extension of the Standard Model. Finally, we comment on potential additional effects due to the more exotic dynamics of overlapping phase transitions.
Highlights
Affecting the amount of baryon asymmetry produced in the NMSSM [15]
This allows for a situation in which phase transitions overlap, such that the later bubbles may nucleate both in high temperature and intermediate temperature phases. Such scenarios may lead to more exotic gravitational wave spectra, which cannot be fitted that of a consecutive PTs. We demonstrate this explicitly in the singlet extension of the Standard Model
In this work we have considered the gravitational wave signatures from multi-step phase transitions
Summary
For a system with multiple scalar fields evolving with temperature during a cosmic phase transition, many thermal properties are controlled by the euclidean action. The transition temperature TN is defined as the temperature when at least one critical bubble forms within a Hubble volume and is approximately given by SE TN. We note that a typical wall velocity is 0.2 ≤ vw ≤ 0.6 for the electroweak transition, but may vary from vw ∼ 0.01 and vw → 1 depending on the medium in which the bubble expands. In a more general scenario the relationship between temperature and time is more involved, as the production of bubbles releases latent heat which reheats the vanilla vacuum. Since the bubble wall velocities are assumed to be relatively fast for our analysis, we do not expect. We will assume that the relevant temperature range in the vanilla vacuum will not be affected by reheating, for the majority of the volume. For an analysis where this assumption is relaxed see [78]
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