2025/05/20 by Mattia Capuano, Livia Ferro, Capuano, Mattia +5 · 3 citations
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2505.14609
openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cosmological correlation functions are central observables in modern cosmology, as they encode properties of the early universe. In this paper, we derive novel canonical differential equations for wavefunction coefficients in power-law FRW cosmologies by combining positive geometries and the combinatorics of tubings of Feynman graphs. First, we establish a general method to derive differential equations for any function given as a twisted integral of a logarithmic differential form. By using this method on a natural set of functions labelled by tubings of a given Feynman diagram, we derive a closed set of differential equations in the canonical form. The coefficients in these equations are related to region variables with the same notion of tubings, providing a uniform combinatorial description of the system of equations. We provide explicit results for specific examples and conjecture that this approach works for any graph.