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Algebraic Approaches to Cosmological Integrals
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Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space wavefunction. The singularities of these cosmological integrals are parameterized by binary hyperplane arrangements. Using different algebraic tools, we shed light on the differential and difference equations satisfied by these integrals. Moreover, we study a multivariate version of partial fractioning of the flat space wavefunction, and propose a graph-based algorithm to compute this decomposition.
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Cited by 2 Pith papers
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On Cosmological Correlators at One Loop
The one-loop triangle in-in correlator of massless scalars in flat space is evaluated in closed form in terms of dilogarithms, with Landau analysis revealing its physical singularities and a partial-energy factorisati...
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All Tree-Level Massive Cosmological Correlators via Spectral Gluing
Tree-level massive de Sitter correlators are constructed by gluing Lauricella-type vertex functions according to graph combinatorics, and the hypergeometric content collapses to rational functions once the dynamical p...
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