The n-wave scattering amplitude for deep-water surface gravity waves in the two-negative-wavenumber sector equals the volume of the hydrotope polytope.
hub Canonical reference
Cosmological Polytopes and the Wavefunction of the Universe
Canonical reference. 100% of citing Pith papers cite this work as background.
19
Pith papers citing it
Background
100% of classified citations
abstract
We present a connection between the physics of cosmological time evolution and the mathematics of positive geometries, roughly analogous to similar connections seen in the context of scattering amplitudes. We consider the wavefunction of the universe in a class of toy models of conformally coupled scalars (with non-conformal interactions) in FRW cosmologies. The contribution of each Feynman diagram to the wavefunction of the universe is associated with a certain universal rational integrand, which we identify as the canonical form of a "cosmological polytope", which have an independent, intrinsic definition, making no reference to physics. The singularity structure of the wavefunction for this model of scalars is common to all theories, and is geometrized by the cosmological polytope. Natural triangulations of the polytope reproduce the path-integral and "old-fashioned perturbation theory" representations of the wavefunction, and we also find new representations of the wavefunction with no extant physical interpretation. We show in suitable examples how symmetries of the cosmological polytope descend to symmetries of the wavefunction, (such as conformal invariance). In cases such as $\phi^3$ theory in $dS_4$, the final wavefunction obtained from integration of the rational functions gives rise to polylogarithms associated with every graph. We give an explicit expression for the symbol of these polylogs, which record the geometry of sequential projections of the cosmological polytope.
hub tools
citation-role summary
background 7
citation-polarity summary
roles
background 7polarities
background 7representative citing papers
Constructs a graphical coaction for all-loop FRW integrals in conformally-coupled scalar theories via twisted (co)homology, with combinatorial description of kinematic flow and a public web app for computation.
Introduces spectral dispersion bootstrap combining dS spectral decomposition and dispersion relations to compute 3- and 4-point loop correlators with massive scalar and vector exchanges.
Introduces weight-shifting matrices for de Sitter diagrams, generalized with Kronecker products to arbitrary tree-level graphs, to derive massless wavefunction coefficients from conformally coupled seeds.
Computes inflationary bispectra and trispectra from tree-level unparticle exchanges using Mellin-Barnes methods and symmetry-based differential equations, revealing that full shapes are needed to distinguish unparticles from light particles.
De Sitter correlators in conformally coupled φ³ theory admit a time-integral representation built from flat-space correlators, revealing intrinsic simplifications including vanishing of odd conjugate-momentum graphs and a smaller symbol alphabet than the corresponding wavefunction coefficients.
A parity-split IBP system for n-propagator families in de Sitter space is identified, along with a conjecture that dlog-form differential equations extend to dS integrands with Hankel functions, verified for the one-loop bubble.
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
The paper derives a correspondence between boundary terms and field redefinitions for cosmological correlators and classifies non-vanishing boundary contributions in massive-exchange diagrams under dS isometries and broken boosts.
Proves asymptotic expectations, variances, and quantitative CLTs for edge counts in cosmological polytopes from ER graphs via graph descriptions and discrete Malliavin-Stein method.
The n-site chain graph contribution to the de Sitter cosmological wavefunction in conformally coupled φ³ theory is expressed explicitly in terms of Rudenko's quadrangular polylogarithms.
Banana loop cosmological correlators are captured by master integrals from tubings of marked graphs, with connection matrices derived from activation, merger, swap, and copy rules unique to unparticle exchanges.
Rigorous proof that rational parts of spinning conformal correlators are spanned by known building blocks, plus combinatorial counts and closed formulas for three-point structures.
The all-loop two-site cosmological wavefunction coefficient admits an equivalent maximal-chain expansion on the Boolean lattice that unifies the shifted-tree decomposition and the tubing construction via finite-difference operators and cubical integrals.
Equal-time correlators are simpler than wavefunctions because full-spacetime integration of propagators eliminates certain poles and yields a vanishing first subleading term in every Laurent expansion around poles.
Adapts BCFW-style recursion to deformed ABHY-associahedron and D-type cluster polytopes for tree-level and one-loop amplitudes in multi-scalar cubic theories.
In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.