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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Cosmological weight-shifting matrices

  • Claire de Korte1
  • Harry Goodhew2,3
  • Kamran Salehi Vaziri4
  • Nicolas Weiss1
4 affiliations
  1. 1Max Planck Institute for Mathematics in the Sciences
  2. 2Leung Center for Cosmology and Particle Astrophysics
  3. 3National Taiwan University
  4. 4University of Amsterdam
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Abstract

We construct matrices that shift the scaling dimension of scalar fields for arbitrary de Sitter Feynman diagrams. Acting on a set of master integrals, these weight-shifting matrices shift the scaling dimensions of individual edges of a given diagram by an integer. They can thus be applied to a broader range of problems and are simpler to implement than earlier derivative-based approaches. By introducing a Kronecker product representation of our matrix formulation, we generalise weight-shifting operators beyond four-point functions to arbitrary tree-level diagrams. As an application, we obtain explicit expressions for several massless wavefunction coefficients in four-dimensional de Sitter space, starting from conformally coupled seed functions. Our construction provides a systematic and graph-local approach to generating cosmologically relevant correlators from simpler master integrals.

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Cite

BibTeXRIS
BibTeX
@article{korte2026cosmological,
  title = {{Cosmological weight-shifting matrices}},
  author = {Claire de Korte and Harry Goodhew and Kamran Salehi Vaziri and Nicolas Weiss},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)037},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)037},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Cosmological weight-shifting matrices
AU  - Claire de Korte
AU  - Harry Goodhew
AU  - Kamran Salehi Vaziri
AU  - Nicolas Weiss
PY  - 2026
DA  - 2026/11/05
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)037
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)037
AB  - We construct matrices that shift the scaling dimension of scalar fields for arbitrary de Sitter Feynman diagrams. Acting on a set of master integrals, these weight-shifting matrices shift the scaling dimensions of individual edges of a given diagram by an integer. They can thus be applied to a broader range of problems and are simpler to implement than earlier derivative-based approaches. By introducing a Kronecker product representation of our matrix formulation, we generalise weight-shifting operators beyond four-point functions to arbitrary tree-level diagrams. As an application, we obtain explicit expressions for several massless wavefunction coefficients in four-dimensional de Sitter space, starting from conformally coupled seed functions. Our construction provides a systematic and graph-local approach to generating cosmologically relevant correlators from simpler master integrals.
SN  - 1029-8479
ER  -