Symmetry breaking and false vacuum decay after hybrid inflation

Abstract

We discuss the onset of symmetry breaking from the false vacuum in generic scenarios in which the mass squared of the symmetry breaking ͑Higgs͒ field depends linearly with time, as it occurs, via the evolution of the inflaton, in models of hybrid inflation. We show that the Higgs fluctuations evolve from quantum to classical during the initial stages. This justifies the subsequent use of real-time lattice simulations to describe the fully nonperturbative and nonlinear process of symmetry breaking. The early distribution of the Higgs field is that of a smooth classical Gaussian random field, and consists of lumps whose shape and distribution is well understood analytically. The lumps grow with time and develop into ''bubbles'' which eventually collide among themselves, thus populating the high momentum modes, in their way towards thermalization at the true vacuum. With the help of some approximations we are able to provide a quasianalytic understanding of this process.

Simulations of Cold Electroweak Baryogenesis: finding the optimal quench time

“…We derive the classical equations of motion by variation of the action, and solve them numerically without further approximation. The initial condition is the vacuum state of the Higgs field, when the Higgs potential is simply 8) and where the field and momentum correlators are each given their zero-point fluctuations, sometimes referred to as the "just the half" initialisation [18][19][20]. We initialise only the unstable modes |k| ≤ µ.…”

Chern-Simons and winding number in a tachyonic electroweak transition

“…we also have n w = 1 2π ∂ x ω. In order to gain some intuition, let us consider the following simple form 15) for which the Higgs length ρ has a minimum when x is close to zero. This configuration is shown in a parametric plot in figure 1.…”

“…which can be solved exactly for the initial stage where µ 2 eff ≈ −M 3 t [28,15] (choosing t = 0 as the onset of the transition). It turns out that the unstable field modes, i.e.…”

“…In [14] it was shown how WMAP data constrain the parameters of a model and it was noted that it might be falsified by the LHC. The transition was studied by analytic and numerical methods [15,16,17,18,19], and the magnitude of the asymmetry generated by a form of CP violation was computed in [16,19].…”

Electroweak-scale inflation, inflaton–Higgs mixing and the scalar spectral index

“…The basic reason for the limit on p is the fact that p > 5 implies a rapid turning down of the potential as σ increases and, together with the low value V 1/4 0 = 100 GeV, Our u is equivalent to the velocity V of [27,11].…”