Domain walls seeding the electroweak phase transition

Abstract

Topological defects can act as local impurities that seed cosmological phase transitions. In this paper we study the case of domain walls, and how they can affect the electroweak phase transition in the Standard Model extended with a Z 2 -odd scalar singlet. When the transition is two-step, the early breaking of the Z 2 symmetry implies the formation of domain walls which can then act as nucleation sites for the second step. We develop a method based on dimensional reduction to calculate the rate of the catalyzed phase transition within the 3d theory on the domain wall surface. By comparison with the standard homogeneous rate, we conclude that the seeded phase transition is generically faster and it ultimately determines the way the phase transition is completed. We comment on the phenomenological implications for gravitational waves and baryogenesis. CONTENTS I. Introduction 1 II. Seeded vs homogeneous vacuum decay 2 III. The SM plus scalar singlet 3 IV. Formalism for the seeded phase transition 4 A. Kaluza-Klein decomposition 4 B. Thin wall approximation 7 V. Results 9 A. The rolling 9 B. The tunneling 11 C. The bubble 12 VI. Discussion 13 Acknowledgements 14 A. Bubble tension in the thin wall approximation 14 B. Estimate of the nucleation temperature 15 References 15

Cosmological defects

“…1 left for a representative benchmark. Here, the seeded bounce action 𝐵 s has been evaluated according to three different methods: within a 2+1 effective field theory living on the domain wall (solid lines from green to blue with increasing level of accuracy) [16], by the thin wall approximation in purple, and by directly solving the equations of motion with reduced symmetry (red diamonds) [18] with the help of the Mountain Pass Theorem (MPT) [24]. In fact, as the presence of the walls breaks rotational invariance, the seeded critical bubble will not be spherical but rather of ellipsoidal shape, complicating the computation of the corresponding action.…”

Ultra-relativistic bubbles from the simplest Higgs portal and their cosmological consequences

“…We can avoid the stable domain walls if we assume some small Z 2 breaking, however in this case the question rises about the timescale for the stability of the domain walls. This is particularly important since recently it was shown [102] that for singlet extension of the SM the domain walls (if still present) will become seeds of the secondary phase transition (0, v s ) → (v h , 0) and will dominate the phase transition. We will follow closely the discussion in the section 4.2 using only the tree level potential and the thermal corrections to the masses.…”

“…The nucleation temperature (T 2D w ) of 2D bounces should be found numerically (Ref. [102]) however it will be obviously smaller than T crit (of (v s , 0) → (v h , 0) phase transition). At this point we can safely ignore the seeded phase transition effects if all of the domain walls annihilate in the interval of temperatures…”

Reviving keV sterile neutrino dark matter

“…Such two-stepped phase transitions, in which the two scalar fields develop their vev's one after the other, have been considered e.g. in [56]. The assumption that the shift in the flavon vev is realised during the EWPT simply allows us to fix the freeze-out temperature to the temperature of the EWPT, i.e.…”