Pith. sign in

REVIEW 13 cited by

Differential Equations for Cosmological Correlators

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2312.05303 v2 pith:VU5XKNF7 submitted 2023-12-08 hep-th

classification hep-th
keywords equationsdifferentialcosmologicalcorrelationsgraphsevolutionintegralsphysics
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and "twist factors" that depend on the cosmological evolution. These integrals are part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict -- by hand -- the equations for all tree graphs. While the rules of this "kinematic flow" are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in ${\rm tr}\,\phi^3$ theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Higher-Spin Correlators in dS

    hep-th 2026-08 accept novelty 8.0 of 10

    The five-point de Sitter higher-spin correlator is shown to be a spurious-singularity-free rational function organized by graph-theoretic orbits of the complete graph K5.

  2. On Cosmological Correlators at One Loop

    hep-th 2026-01 conditional novelty 8.0 of 10

    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...

  3. Anatomy of Family Trees in Cosmological Correlators

    hep-th 2025-09 conditional novelty 8.0 of 10

    A complete map of singularities and local series expansions for the hypergeometric building blocks of tree-level cosmological correlators.

  4. A physical basis for cosmological correlators from cuts

    hep-th 2024-11 conditional novelty 8.0 of 10

    The physical subspace of FRW wavefunction integrals is characterized by shared cuts/residues, and the authors supply cut-tubing rules that enumerate its basis graphically.

  5. All Tree-Level Massive Cosmological Correlators via Spectral Gluing

    hep-th 2026-07 conditional novelty 7.0 of 10

    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...

  6. Cosmological Correlators in KLF and the Double-Exchange

    hep-th 2026-07 conditional novelty 7.0 of 10

    The double-exchange cosmological correlator is computed in KLF space, yielding a double series over hypergeometric functions that improves on prior four-layer representations.

  7. Bootstrapping the Cosmological Collider with Resonant Features

    hep-th 2025-05 conditional novelty 7.0 of 10

    Oscillatory couplings with frequency above the heavy field mass remove the Boltzmann suppression of cosmological collider signals and produce new scale-dependent bispectrum shapes, with axion monodromy as a concrete r...

  8. Geometry of Kinematic Flow

    hep-th 2025-04 conditional novelty 7.0 of 10

    The wavefunction coefficients of conformally coupled scalars in power-law cosmologies obey differential equations whose basis functions can be arranged on hypercubes and zonotopes, with a single merger rule generating...

  9. Massive Inflationary Amplitudes: Differential Equations and Complete Solutions for General Trees

    hep-th 2024-12 conditional novelty 7.0 of 10

    Every tree-level massive inflation correlator in the signal region can be written as one massive family tree series plus its cuts, with 2I summation variables.

  10. Euler Discriminant of Complements of Hyperplanes

    math.AG 2024-11 conditional novelty 7.0 of 10

    The Euler discriminant of families of hyperplane complements is the zero set of an explicit product of determinants indexed by connected square subgraphs.

  11. Correlators are simpler than wavefunctions

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    Equal-time correlators are simpler than wavefunctions because they come from full-spacetime integrals; this implies fewer poles, cleaner factorization, and a systematic pole expansion whose first subleading term vanishes.

  12. A non-perturbative construction of the de Sitter late-time boundary

    hep-th 2024-11 conditional novelty 6.0 of 10

    The paper derives an inversion formula that defines de Sitter boundary operators as integrals of bulk fields against the bulk-to-boundary propagator, reproducing known two-point functions and perturbation theory.

  13. Cosmological Correlators at the Loop Level

    hep-th 2024-11 conditional novelty 6.0 of 10

    Using the partial Mellin-Barnes method, the author derives analytic signals from one-loop bubble diagrams in inflation correlators, including the first analytic results for a de Sitter boost-breaking bubble.

Pith tools