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Towards the non-perturbative cosmological bootstrap
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abstract
We study quantum field theory on a de Sitter spacetime dS$_{d+1}$ background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group $SO(d+1,1)$. As the first application of the Hilbert space formalism, we recover the K\"allen-Lehmann spectral decomposition of the scalar bulk two-point function. In the process, we exhibit a relation between poles in the corresponding spectral densities and the boundary CFT data. Moreover, we derive an inversion formula for the spectral density through analytical continuation from the sphere and use it to find the spectral decompisiton for a few examples. Next, we study the conformal partial wave decomposition of the four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity properties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in dS$_2$.
Forward citations
Cited by 13 Pith papers
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Higher-Spin Correlators in dS
The five-point de Sitter higher-spin correlator is shown to be a spurious-singularity-free rational function organized by graph-theoretic orbits of the complete graph K5.
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Ising the way into de Sitter
The two-dimensional thermal Ising model on de Sitter provides exact cosmological correlators that stay finite at late times, with perturbative secular logarithms resummed into principal-series oscillations.
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On Cosmological Correlators at One Loop
The one-loop triangle in-in correlator of massless scalars in flat space is evaluated in closed form in terms of dilogarithms, with Landau analysis revealing its physical singularities and a partial-energy factorisati...
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Cosmological Correlators in KLF and the Double-Exchange
The double-exchange cosmological correlator is computed in KLF space, yielding a double series over hypergeometric functions that improves on prior four-layer representations.
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Propagator positivity bounds for cosmological correlators
An infinite tower of two-sided positivity bounds constrains the EFT coefficients of heavy fields on de Sitter, ruling out correlators with no unitary/causal UV completion.
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Geometry of Kinematic Flow
The wavefunction coefficients of conformally coupled scalars in power-law cosmologies obey differential equations whose basis functions can be arranged on hypercubes and zonotopes, with a single merger rule generating...
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A microscopic realization of dS$_3$
Pure dS3 quantum gravity is claimed to be dual to the complex Liouville string's matrix integral, with integrated cosmological correlators equal to resolvent correlators and de Sitter entropy equal to 2 log of the eig...
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Effective Field Theory and In-In Correlators
Matching in-in correlators between a full theory and its effective theory requires extra boundary terms in flat space, but those terms fade away in de Sitter space.
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A discrete series gauge field at the late-time boundary of $dS_4$
Both Δ=1 and Δ=2 late-time Maxwell operators on planar dS4 furnish the photon unitary discrete series of SO(4,1), which splits into opposite-helicity summands via self-dual field-strength sectors.
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Cosmological Correlators in Gauge Theory and Gravity from EAdS
Gauge and gravitational late-time correlators in de Sitter are mapped to EAdS Witten diagrams, with new Mellin-space propagators and a treatment of even boundary dimensions.
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Cosmological correlators in gravitationally-constrained de Sitter states
Cosmological correlators in gravitationally constrained de Sitter states are conformally invariant and differ from QFT vacuum correlators, but relational observables with a heavy background state can reproduce QFT results.
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A non-perturbative construction of the de Sitter late-time boundary
The paper derives an inversion formula that defines de Sitter boundary operators as integrals of bulk fields against the bulk-to-boundary propagator, reproducing known two-point functions and perturbation theory.
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Cosmological Correlators at the Loop Level
Using the partial Mellin-Barnes method, the author derives analytic signals from one-loop bubble diagrams in inflation correlators, including the first analytic results for a de Sitter boost-breaking bubble.
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