引力波动背景下的突现自发对称性破缺和突现对称性恢复
Emergent spontaneous symmetry breaking and emergent symmetry restoration in rippling gravitational background
摘要：
我们研究了波纹引力背景对具有双势阱的标量场的影响，着重于与著名的卡皮查摆动力学的类比。波纹呈现为尺度因子的无穷小但快速振荡的扰动。我们发现，由此产生的动力学关键取决于在$ξ\,R\, ϕ^2$顶点的参数$ξ$的值。对于适当形式的含时扰动，所产生的有效作用量通常是协变的，并且在足够高的频率下，在$ξ<0$和$ξ>1/6$处，有效势在零处具有单个最小值，从而自发地恢复基态的对称性破缺。另一方面，在$0<ξ< 1/6$中，即使在未扰动的情况下不存在对称性破缺，也会出现自发对称性破缺。
英文摘要：
We study effects of a rippling gravitational background on a scalar field with a double well potential, focusing on the analogy with the well known dynamics of the Kapitza's pendulum. The ripples are rendered as infinitesimal but rapidly oscillating perturbations of the scale factor. We find that the resulting dynamics crucially depends on a value of the parameter $ξ$ in the $ξ\,R\, ϕ^2$ vertex. For the time-dependent perturbations of a proper form the resulting effective action is generally covariant, and at a high enough frequency at $ξ<0$ and at $ξ>1/6$ the effective potential has a single minimum at zero, thereby restoring spontaneously broken symmetry of the ground state. On the other side, at $0<ξ< 1/6$ spontaneous symmetry breaking emerges even when it is absent in the unperturbed case.
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