We consider the Abelian Higgs model in the broken phase as a spectator in cosmological spaces of general $D$ space-time dimensions, and allow for the condensate to be time-dependent. We fix the unitary gauge using Dirac's formalism for constrained systems, and then quantize the gauge-fixed system. Vector and scalar perturbations develop time-dependent masses. We work out their propagators assuming the cosmological background is that of power-law inflation, characterized by a constant principal slow-roll parameter, and that the scalar condensate is in the attractor regime, scaling as the Hubble rate. Our propagators correctly reduce to known results in the Minkowski and de Sitter space limits. We use the vector propagator to compute the equal-time correlators of electric and magnetic fields and find that at super-Hubble separations the former is enhanced, while the latter is suppressed compared to the vacuum fluctuations of the massless vector field. These correlators satisfy the hierarchy governed by Faraday's law.

中文翻译：

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幂律膨胀中的阿贝尔希格斯模型：幺正规范中的传播子

我们将破碎相中的阿贝尔希格斯模型视为一般 $D$ 时空维度的宇宙空间中的旁观者，并允许凝聚物与时间相关。我们使用狄拉克的约束系统形式主义来固定单一规范，然后量化规范固定系统。矢量和标量扰动会产生与时间相关的质量。我们计算出他们的传播子，假设宇宙学背景是幂律暴胀的背景，其特征是恒定的主要慢滚参数，并且标量凝聚体处于吸引子状态，按哈勃速率缩放。我们的传播器在 Minkowski 和 de Sitter 空间限制中正确地减少到已知结果。我们使用矢量传播器来计算电场和磁场的等时相关器，发现在超哈勃分离时，前者被增强，而后者与无质量矢量场的真空波动相比被抑制。这些相关器满足法拉第定律所管辖的层次结构。