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Title: The cosmological bootstrap: inflationary correlators from symmetries and singularities

Abstract

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. Wemore » explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.« less

Authors:
 [1];  [2];  [3];  [2]
+ Show Author Affiliations
  1. Institute for Advanced Study, Princeton, NJ (United States)
  2. University of Amsterdam (The Netherlands)
  3. Harvard University, Cambridge, MA (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States); Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1839905
Alternate Identifier(s):
OSTI ID: 1801996
Grant/Contract Number:  
SC0009988; SC0019018
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Cosmology of Theories beyond the SM; Effective Field Theories; Models of Quantum Gravity; Space-Time Symmetries; Physics

Citation Formats

Arkani-Hamed, Nima, Baumann, Daniel, Lee, Hayden, and Pimentel, Guilherme L. The cosmological bootstrap: inflationary correlators from symmetries and singularities. United States: N. p., 2020. Web. doi:10.1007/jhep04(2020)105.
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Arkani-Hamed, Nima, Baumann, Daniel, Lee, Hayden, & Pimentel, Guilherme L. The cosmological bootstrap: inflationary correlators from symmetries and singularities. United States. https://doi.org/10.1007/jhep04(2020)105
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Arkani-Hamed, Nima, Baumann, Daniel, Lee, Hayden, and Pimentel, Guilherme L. Fri . "The cosmological bootstrap: inflationary correlators from symmetries and singularities". United States. https://doi.org/10.1007/jhep04(2020)105. https://www.osti.gov/servlets/purl/1839905.
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@article{osti_1839905,
title = {The cosmological bootstrap: inflationary correlators from symmetries and singularities},
author = {Arkani-Hamed, Nima and Baumann, Daniel and Lee, Hayden and Pimentel, Guilherme L.},
abstractNote = {Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.},
doi = {10.1007/jhep04(2020)105},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2020,
place = {United States},
year = {Fri Apr 17 00:00:00 EDT 2020},
month = {Fri Apr 17 00:00:00 EDT 2020}
}
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