The cosmological bootstrap: inflationary correlators from symmetries and singularities

By N. Arkani-Hamed, D. Baumann, Hayden Lee, G. L. Pimentel. Journal of High Energy Physics, 2018

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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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d53f322f2fe0bd29d9ac56b317a4598de975004

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Citations in the corpus

Planck 2018 results. IX. Constraints on primordial non-Gaussianity (2019, background): “Measuring primordial NG can allow us to pin down masses and spins of the particle content present during inflation, making inflation a powerful cosmological collider (Chen 2010b; Chen & Wang 2010; Noumi et al. 2013; Arkani-Hamed & Maldacena 2015; Baumann et al. 2018; Arkani-Hamed et al. 2018).”
The Cosmological Optical Theorem (2020, background): “This would generalize the very interesting results recently derived in [9, 21, 24] using de Sitter isometries to more phenomenologically interesting models.”
The Cosmological Bootstrap: Spinning correlators from symmetries and factorization (2020, methodology): “In [47], the bootstrap philosophy was applied to the study of inflationary scalar correlators (see also [48–54] for related work).”
Building a boostless bootstrap for the bispectrum (2020, methodology): “Indeed, we know from [10, 20] (see also the discussions in [14, 19]) that the ζ bispectrum arises from the “graviton-exchange” scalar trispectrum29 after “putting a leg on the background”, i.”
The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “In [1], the solutions of (2.”
CMB-S4 Science Case, Reference Design, and Project Plan (2019, background): “Heavy degrees of freedom do not fluctuate appreciably, but may come into existence by quantum fluctuations and decay into inflaton quanta, generating non-Gaussian correlations [85, 86, 29, 87].”