Cosmological Weight-Shifting Matrices

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.

48 pages