Cosmological correlators through the looking glass: reality, parity, and factorisation

Stefanyszyn, David; Tong, Xi; Zhu, Yuhang

Abstract

We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all n-point functions and allow for the exchange of additional states of any mass and integer spin. Our proof makes use of a decomposition of the inflationary bulk-bulk propagator of massive spinning fields which preserves UV-convergence and ensures that the time-ordered contributions are purely real after we rotate to Euclidean time. We use this reality property to show that the maximally-connected parts of wavefunction coefficients, from which total-energy singularities originate, are purely real. In a theory where all states are in the complementary series, this reality extends to the full wavefunction coefficient. We then use our reality theorem to show that parity-odd correlators (correlators that are mirror asymmetric) are factorised and do not diverge when the total-energy is conserved. We pay special attention to the parity-odd four-point function (trispectrum) of inflationary curvature perturbations and use our reality/factorisation theorems to show that this observable is factorised into a product of cubic diagrams thereby enabling us to derive exact shapes. We present examples of couplings between the inflaton and massive spin-1 and spin-2 fields, with the parity-violation in the trispectrum driven by Chern-Simons corrections to the spinning field two-point function, or from parity-violating cubic interactions which we build within the Effective Field Theory of Inflation. In addition, we present a first-of-its-kind example of a parity-violating trispectrum, generated at tree-level, that arises in a purely scalar theory where the inflaton mixes linearly with an additional massive scalar field.

Citation

Stefanyszyn, D., Tong, X., & Zhu, Y. (2024). Cosmological correlators through the looking glass: reality, parity, and factorisation. Journal of High Energy Physics, 2024, Article 196. https://doi.org/10.1007/jhep05%282024%29196

• Journal Article Type: Article
• Acceptance Date: Apr 15, 2024
• Online Publication Date: May 16, 2024
• Publication Date: May 16, 2024
• Deposit Date: Jul 24, 2024
• Publicly Available Date: Jul 25, 2024
• Journal: Journal of High Energy Physics
• Electronic ISSN: 1029-8479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Article Number: 196
• DOI: https://doi.org/10.1007/jhep05%282024%29196
• Keywords: Discrete Symmetries, de Sitter space
• Public URL: https://nottingham-repository.worktribe.com/output/35425645
• Publisher URL: https://link.springer.com/article/10.1007/JHEP05(2024)196
• Additional Information: Received: 20 October 2023; Accepted: 15 April 2024; First Online: 16 May 2024