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.
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Acknowledgments
We thank Paolo Benincasa, Zongzhe Du, Sadra Jazayeri, Austin Joyce, Hayden Lee, Arthur Lipstein, Scott Melville, Enrico Pajer, Sébastien Renaux-Petel, Denis Werth, Yi Wang, Zhong-Zhi Xianyu and Yang Zhang for helpful discussions. D.S. is supported by a UKRI Stephen Hawking Fellowship [grant number EP/W005441/1] and a Nottingham Research Fellowship from the University of Nottingham. XT and YZ are supported in part by the National Key R&D Program of China (No. 2021YFC2203100). XT is also supported by STFC consolidated grants ST/T000694/1 and ST/X000664/1. D.S. thanks The Hong Kong University of Science and Technology for kind hospitality. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising. YZ is also is supported by the IBS under the project code, IBS-R018-D3.
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Stefanyszyn, D., Tong, X. & Zhu, Y. Cosmological correlators through the looking glass: reality, parity, and factorisation. J. High Energ. Phys. 2024, 196 (2024). https://doi.org/10.1007/JHEP05(2024)196
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DOI: https://doi.org/10.1007/JHEP05(2024)196