近日，印度理工学院坎普尔分校的Nilay Kundu及其研究团队取得一项新进展。经过不懈努力，他们揭示α真空中的暴胀非高斯性及共形对称一致性。相关研究成果已于2024年10月22日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队研究了在单场慢滚暴胀中，与非本奇-戴维斯初始状态（即α-真空态）中标量涨落相关的暴胀非高斯性的共形不变性。α-真空态是一个包含本奇-戴维斯态的单参数态族，它在近德西特时空中保留了暴胀动力学的共形对称性。

在主要慢滚近似的框架下，研究人员使用“in-in”形式主义计算了α-真空态中的四点标量相关函数（即三谱）。研究人员验证了三点和四点标量α-真空态相关函数之间满足共形沃德恒等式。令人惊讶的是，这与先前报道的两点和三点相关函数之间违反沃德恒等式的负面结果形成了对比。

此外，研究人员还扩展了先前用于计算具有本奇-戴维斯初始条件的，相关函数的波函数方法，以计算α-真空态中的三点和四点标量相关函数。通过波函数方法得到的结果与相应的“in-in”结果一致，这进一步验证了他们使用α-真空态相关函数检查沃德恒等式的合理性。

附：英文原文

Title: Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries

Author: Ansari, Arhum, Banerjee, Pinak, Dhivakar, Prateksh, Jain, Sachin, Kundu, Nilay

Issue&Volume: 2024-10-22

Abstract: We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as the α-vacuum, in single-field slow-roll inflation. The α-vacuum is a one-parameter family of states, including the Bunch-Davies one, that preserves the conformal symmetry of inflationary dynamics in a nearly de-Sitter space-time. Working within the leading slow-roll approximation, we compute the four-point scalar correlator (the trispectrum) in α-vacuum using the in-in formalism. We check that the conformal Ward identities are met between the three and four-point scalar α-vacua correlators. Surprisingly, this contrasts the previously reported negative result of the Ward identities being violated between the two and the three-point correlators. We have also extended the wave-functional method, previously used for correlators with Bunch-Davies initial condition, to compute the three and four-point scalar correlators in α-vacua. The results obtained from the wave-function method match the corresponding in-in results, adding further justification to our check of Ward identities with α-vacua correlators.

DOI: 10.1007/JHEP10(2024)147

Source: https://link.springer.com/article/10.1007/JHEP10(2024)147