发表机构
Jadavpur University（贾达普大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究暴胀德西特时空中相互作用旁观者标量场在红外流下的行为，通过Schwinger-DeWitt和精确传播子计算有效势，发现流驱动对称恢复，并分析功率谱与谱指数变化。
AI 中文摘要
在本工作中，我们研究了暴胀早期宇宙关联函数在红外标度流下的行为，针对相互作用的旁观者标量场理论。我们首先在暴胀德西特时空中推导了φ^4、φ^4-汤川以及破缺相O(N)模型的单圈有效势，分别使用局域Schwinger-DeWitt展开传播子和精确的德西特传播子。Schwinger-DeWitt展开在亚哈勃长度尺度上有效，为确定具有亚哈勃康普顿波长的高能现象的前沿曲率修正提供了合适的框架。这些有效势表现出自发对称破缺的模式，随后被用作Wetterich方程中的紫外边界条件，以生成所需的红外流。该流被证明驱动理论趋向于对称恢复。利用这些红外改进的有效势，我们计算了旁观者标量时间重合两点关联函数的随机功率谱和谱指数。我们表明，上述两种传播子对应的结果在定性上大致一致，但在定量上可能存在显著差异。两者在深红外区域对φ^4和φ^4-汤川均显示出谱指数的增加。强调了费米子相互作用的影响。此外，对于O(N)标量，我们证明了随着N变大，有效势的形状对流的敏感性越来越低。讨论了这对关联函数的影响。
英文摘要
In this work we investigate the behaviour of early inflationary cosmic correlation functions under the flow of the infrared scale for interacting spectator scalar field theories. We start with the derivation of the one-loop effective potentials for $ϕ^4$, $ϕ^4$-Yukawa and broken phase $O(N)$ model in the inflationary de Sitter spacetime, first using the local Schwinger-DeWitt expansion propagator, and next using the exact de Sitter propagator. The Schwinger-DeWitt expansion being valid in a sub-Hubble length scale, furnishes suitable framework to determine the leading curvature corrections to high energy phenomena having sub-Hubble Compton wavelengths. These effective potentials show spontaneous symmetry breaking pattern, and are next used as ultraviolet boundary conditions in the Wetterich equation generating the desired IR flow. The flow is shown to drive the theory towards symmetry restoration. Using these IR-improved effective potentials, we next compute the stochastic power spectra and spectral indices for the temporally coincident two point correlation function of the spectator scalar. We show that the results corresponding to the aforementioned two kind of propagators are roughly in qualitative agreement with each other, but may differ quantitatively significantly. Both of them show increase in the spectral index in the deep IR for $ϕ^4$ and $ϕ^4$-Yukawa. The effect of fermionic interaction has been emphasised. Also for the case of the $O(N)$ scalar, we demonstrate that the effective potential's shape becomes more and more insensitive to the flow as $N$ gets large. Implication of this on the correlation function has been discussed.
Commentsv1, 27 pp, 8 figs.;
