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The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization

by Daniel Baumann, Carlos Duaso Pueyo, Austin Joyce, Hayden Lee, Guilherme L. Pimentel

This Submission thread is now published as SciPost Phys. 11, 071 (2021)

Submission summary

As Contributors: Guilherme L. Pimentel · Hayden Lee
Arxiv Link: (pdf)
Date accepted: 2021-08-23
Date submitted: 2021-07-25 23:42
Submitted by: L. Pimentel, Guilherme
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Cosmology and Nongalactic Astrophysics
Approach: Theoretical


We extend the cosmological bootstrap to correlators involving massless particles with spin. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three- and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.

Published as SciPost Phys. 11, 071 (2021)

Reports on this Submission

Anonymous Report 2 on 2021-8-5 (Invited Report)


Thanks to the authors for their clarifications and modifications. I am happy to recommend their paper for publication.

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Anonymous Report 1 on 2021-7-27 (Invited Report)


The authors have properly addressed my previous questions. I am happy to recommend the paper for publication at SciPost. Congratulations to the authors for a very nice piece of work.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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Anonymous on 2021-08-13  [id 1669]


  1. I understand that the boundary correlators computed in this paper rely on the fact that the background is not a truly time-dependent cosmological spacetime, like an FRW spacetime or even those with less isometries. Is it possible to generalize the approach of the authors to include genuine cosmological backgrounds ?

  2. It appears that at this stage the results are not yet in a stage of development where they can be compared with cosmological observational data, say, for instance on non-Gaussianity. Is there a path to such a development ?