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首页早期宇宙希格斯-胀气耦合与真空稳定性:新界限研究
本文主要探讨了希格斯-胀气耦合在早期宇宙中电弱真空稳定性的影响,特别是在充气(即宇宙膨胀期间)和预热(即宇宙扩张后粒子生成过程)这两个关键时期。希格斯场的动态行为在早期宇宙中起着决定性作用,尤其是在高能物理中,微小的希格斯-胀气相互作用可能会对电弱标准模型中的真空状态产生显著影响。 在实际的再热模型中,这种耦合不仅体现在三线性(trilinear)水平,即希格斯、胀气子和另一个粒子的相互作用,也包括四次(quartic)级的相互作用,这是由于在粒子生成过程中,非线性效应不能忽视。作者的研究特别关注了参数共振(parametric resonance)和速动共振(tachyonic resonance),这两种现象在预热阶段能够引起希格斯场的强烈振荡,可能导致原本稳定的电弱真空变得不稳定。 作者通过使用先进的数值工具,如晶格模拟技术,来分析和模拟这些过程。他们的研究结果显示,如果希格斯和胀气子之间的相互作用过于剧烈,超过了特定的阈值,就可能触发真空不稳定性的危机。因此,他们得出了一个关键的结论:在充气和预热时期,为了确保宇宙的稳定演化,希格斯与胀气子之间的四次和三线性相互作用必须被限制在安全的范围内。 这项工作对于理解宇宙早期的物理过程具有重要意义,它不仅加深了我们对希格斯机制的理解,还为宇宙学模型中的参数设定提供了重要约束。开放存取期刊《宇宙学和高能物理杂志》(Journal of Cosmology and Astroparticle Physics)在2016年11月发布了这篇研究成果,为理论物理学界提供了关于早期宇宙中希格斯-胀气耦合的最新见解。
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JCAP11(2016)025
where
p
hh
2
i plays the role of the relevant energy scale at which the coupling should be
evaluated. Since we are only interested in the high energy regime, in our numerical analysis
we use the step-function approximation
λ
h
(µ) = 0.01 × sign
h
SM
c
−
p
hh
2
i
, (2.8)
where h
SM
c
∼ 10
10
GeV is the critical scale of the Standard Model at which λ
h
flips sign.
3 Pure parametric resonance
Let us first consider the case where the trilinear interaction is negligible, σ
hφ
≈ 0. The
Higgs-inflaton interaction is quartic so that we recover the well-known parametric resonance
setting [16].
The equations of motion for the Higgs field are quadratic in h apart from the quartic
self-interaction. During the parametric resonance regime, the effect of the latter can be
approximated as h
4
→ 6h
2
hh
2
i, which is known as the Hartree approximation. In that case,
the equations of motion for different momentum modes decouple. In terms of the rescaled
Higgs momentum modes X
k
≡ a
3/2
h
k
, where a is the scale factor, one has [16]
¨
X
k
+ ω
2
k
X
k
= 0 with ω
2
k
=
k
2
a
2
+
λ
hφ
2
Φ
2
cos
2
(mt) + 3λ
h
a
−3
hX
2
i +
3
2
wH
2
. (3.1)
In the last term, w = p/ρ = −
1 +
2
3
˙
H
H
2
is the equation of state parameter of the Universe,
which vanishes in the matter-like background. We thus neglect this term.
If the Higgs-inflaton coupling λ
hφ
is substantial, the Higgs modes experience amplifica-
tion due to broad parametric resonance. The parameter characterizing the strength of the
resonance is
q(t) =
λ
h
Φ
2
(t)
2m
2
(3.2)
such that q 1 corresponds to the broad resonance regime. In this case, the modes grow
exponentially leading to a large Higgs field variance hh
2
i. The fluctuations can be so signif-
icant that they exceed the size of the barrier separating the electroweak vacuum from the
catastrophic one at large field values. In this case, vacuum destabilization occurs. In what
follows, we will estimate the corresponding critical size of λ
hφ
.
As was shown in [16], in the broad resonance regime the Higgs modes evolve adiabatically
away from the inflaton zero-crossings and can be described by the WKB approximation
X
k
'
α
k
√
2ω
k
e
−i
R
ω
k
dt
+
β
k
√
2ω
k
e
i
R
ω
k
dt
, (3.3)
where α
k
, β
k
are some constants. Adiabaticity is broken for certain modes near the inflaton
zero-crossing, where the frequency ω
k
evolves very quickly. There the system can be treated
in analogy to the Schr¨odinger equation as a scattering of plane wave solutions. The adiabatic
constants α
k
and β
k
can be thought of as Bogolyubov coefficients. We assume a vacuum
initial condition for the Higgs modes with α
k
= 1 and β
k
= 0. The occupation number of
Higgs quanta after j ' mt/π zero crossings is then
n
j+1
k
= |β
j+1
k
|
2
(3.4)
– 4 –
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