Precision calculation of inflation correlators at one loop

Lian-Tao Wang,Zhong-Zhi Xianyu,Yi-Ming Zhong

doi:10.1007/jhep02(2022)085

Lian-Tao Wang, Zhong-Zhi Xianyu + Show 1 more

Open Access

https://doi.org/10.1007/jhep02(2022)085

Copy DOI

Abstract

We initiate a systematic study of precision calculation of the inflation correlators at the 1-loop level, starting in this paper with bosonic 1-loop bispectrum with chemical-potential enhancement. Such 1-loop processes could lead to important cosmological collider observables but are notoriously difficult to compute due to the lack of symmetries. We attack the problem from a direct numerical approach based on the real-time Schwinger-Keldysh formalism and show full numerical results for arbitrary kinematics containing both the oscillatory “signals” and the “backgrounds”. Our results show that, while the non-oscillatory part can be one to two orders of magnitude larger, the oscillatory signal can be separated out by applying appropriate high-pass filters. We have also compared the result with analytic estimates typically adopted in the literature. While the amplitude is comparable, there is a non-negligible deviation in the frequency of the oscillatory part away from the extreme squeezed limit.

Highlights

We initiate a systematic study of precision calculation of the inflation correlators at the 1-loop level, starting in this paper with bosonic 1-loop bispectrum with chemical-potential enhancement
The 1-loop 3-point correlator is the sum of contributions from all SK diagrams, S(k1, k2, k3) = a,b=± Sab = 2Re S++ + 2Re S+−, where we applied the reality condition in the last equality
We performed a systematic study of the numerical evaluation of the inflation correlators at the 1-loop level

Summary

Introduction

Due to the enlarged symmetry of dS relative to a general slow-roll background, it is possible to transform a flat-space correlator into the corresponding object in dS via dS time translation and boosts, a process called “cosmological bootstrap”. This technique is very useful for the process that respects the full dS symmetry. Our current understanding of these loop processes is only based on analytical approximations that might be applicable in special limits, but are not fully justified in more general cases In view of this situation, it is desirable to have a fully controlled numerical computation for such processes

Objectives

Results

Conclusion