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The Geometry of Cosmological Correlators

by Paolo Benincasa, Gabriele Dian

Submission summary

Authors (as registered SciPost users): Gabriele Dian
Submission information
Preprint Link:  (pdf)
Date submitted: 2024-03-07 17:36
Submitted by: Dian, Gabriele
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We provide a first principle definition of cosmological correlation functions for a large class of scalar toy models in arbitrary FRW cosmologies, in terms of novel geometries we name {\it weighted cosmological polytopes}. Each of these geometries encodes a universal rational integrand associated to a given Feynman graph. In this picture, all the possible ways of organising, and computing, cosmological correlators correspond to triangulations and subdivisions of the geometry, containing the in-in representation, the one in terms of wavefunction coefficients and many others. We also provide two novel contour integral representations, one connecting higher and lower loop correlators and the other one expressing any of them in terms of a building block. We study the boundary structure of these geometries allowing us to prove factorisation properties and Steinmann-like relations when single and sequential discontinuities are approached. We also show that correlators must satisfy novel vanishing conditions. As the weighted cosmological polytopes can be obtained as an orientation-changing operation onto a certain subdivision of the cosmological polytopes encoding the wavefunction of the universe, this picture allows us to sharpen how the properties of cosmological correlators are inherited from the ones of the wavefunction. From a mathematical perspective, we also provide an in-depth characterisation of their adjoint surface.

Current status:
In refereeing

Reports on this Submission

Anonymous Report 1 on 2024-4-30 (Invited Report)


See attached pdf. I recommend the paper for publication and have some minor questions for the authors which they can choose to expand upon if they feel would enhance the presentation.



Publish (surpasses expectations and criteria for this Journal; among top 10%)

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