天空中的BCS：暴胀费米子凝聚的特征
BCS in the Sky: Signatures of Inflationary Fermion Condensation
AI总结：
本文研究暴胀背景中类BCS费米子凝聚机制，首次计算含曲率效应的非微扰有效势，揭示其一阶相变性质，并预言其在原初非高斯性和随机引力波中的独特观测特征。
摘要：
我们考虑在暴胀背景下的一个类Bardeen-Cooper-Schrieffer（BCS）模型。我们证明，在存在轴化学势的情况下，吸引性的四次费米子自相互作用可以导致类BCS凝聚。在暴胀的刚性de Sitter（dS）极限中，忽略来自暴胀子和引力子的反作用，我们首次计算了在化学势存在下包含完整时空曲率效应的非微扰有效势，该计算基于平均场近似，其有效性已通过Ginzburg判据检验。当变化的Hubble参数被解释为dS时空的有效Gibbons-Hawking温度时，相应的BCS相变总是一阶的。在凝聚相中，该理论可以分别从紫外（UV）和红外（IR）两侧理解为费米性的和玻色性的。这导致曲率扰动的原初非高斯性中出现独特的特征。即，振荡的宇宙对撞机信号在有限的动量比处被平滑地关闭，因为不同的动量比有效地探测不同的能量尺度。此外，这种BCS相变还可以产生随机引力波，这对未来实验是可行的。
英文摘要：
We consider a Bardeen-Cooper-Schrieffer (BCS)-like model in the inflationary background. We show that with an axial chemical potential, the attractive quartic fermion self-interaction can lead to a BCS-like condensation. In the rigid-de Sitter (dS) limit of inflation where backreaction from the inflaton and graviton is neglected, we perform the first computation of the non-perturbative effective potential that includes the full spacetime curvature effects in the presence of the chemical potential, subject to the mean-field approximation whose validity has been checked via the Ginzburg criterion. The corresponding BCS phase transition is always first-order, when the varying Hubble is interpreted as an effective Gibbons-Hawking temperature of dS spacetime. In the condensed phase, the theory can be understood from UV and IR sides as fermionic and bosonic, respectively. This leads to distinctive signatures in the primordial non-Gaussianity of curvature perturbations. Namely, the oscillatory cosmological collider signal is smoothly turned off at a finite momentum ratio, since different momentum ratios effectively probe different energy scales. In addition, such BCS phase transitions can also source stochastic gravitational waves, which are feasible for future experiments.
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