Cosmology meets cohomology

Abstract

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated \emph{relative} twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

36+3 pages, 8 figures; included ancillary files; Journal version

References in corpus (10)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Lectures on differential equations for Feynman integrals
• D-dimensional unitarity cut method
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Integral Coefficients for One-Loop Amplitudes
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Monodromy relations from twisted homology
• Intersection theory rules symbology

Cited by in corpus (14)

• Cosmological Correlators Through the Looking Glass: Reality, Parity, and Factorisation
• Searching for Cosmological Collider in the Planck CMB Data
• Canonical Differential Equations Beyond Genus One
• On one-loop corrections to the Bunch-Davies wavefunction of the universe
• Towards Systematic Evaluation of de Sitter Correlators via Generalized Integration-By-Parts Relations
• A double copy from twisted (co)homology at genus one
• The Massive Flat Space Limit of Cosmological Correlators
• Self-duality from twisted cohomology
• Multivariate hypergeometric solutions of cosmological (dS) correlators by $\text{d}\log$-form differential equations
• Intersection Numbers from Companion Tensor Algebra
• Twisted Riemann bilinear relations and Feynman integrals
• A Note on Kinematic Flow and Differential Equations for Two-Site One-Loop Graph in FRW Spacetime
• General Relativity from Intersection Theory
• Differential equations for tree--level cosmological correlators with massive states