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.
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Differential Equations for Massive Correlators
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abstract
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we express the Feynman integrals underlying cosmological correlators as twisted integrals of rational functions. In this formulation, the integrals belong to a finite set of master integrals obeying a first-order system of differential equations, which can be derived efficiently in the time-integral representation. We show that these equations admit a simple graphical description in terms of graph tubings, which encode the couplings among basis functions and the evolution of singularities. This structure provides an efficient algorithm to derive the differential equations, and a boundary-centric perspective on massive cosmological correlators in which their analytic structure emerges from underlying combinatorial data. As an illustration, we solve the system in the limits of small and large masses.
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UNVERDICTED 10representative citing papers
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.
Exact fermionic bubble loop signals in cosmological collider physics are obtained via spectral and Mellin-Barnes methods, with the Yukawa bispectrum vanishing identically due to field redefinition.
Four-point wavefunction coefficients for external conformally coupled scalars exchanging a particle of generic mass and spin are expressed in closed form as hypergeometric functions of Mandelstam invariants times Legendre polynomials in the cosmological Grassmannian.
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.
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.
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.
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.
citing papers explorer
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On-Shell Bootstrap of Loop Inflation Correlators with Spectral Dispersion
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.
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Cosmological Weight-Shifting Matrices
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.
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Fermionic Bubble Loop in Cosmological Collider Revisited: Exact signals from spectral and Mellin-Barnes methods
Exact fermionic bubble loop signals in cosmological collider physics are obtained via spectral and Mellin-Barnes methods, with the Yukawa bispectrum vanishing identically due to field redefinition.
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Cosmological Collider in the Grassmannian
Four-point wavefunction coefficients for external conformally coupled scalars exchanging a particle of generic mass and spin are expressed in closed form as hypergeometric functions of Mandelstam invariants times Legendre polynomials in the cosmological Grassmannian.
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On the simplicity of de Sitter correlators
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.
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Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations
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.
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de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs
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.
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Kinematic Flow for Banana Loops and Unparticles
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.
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A Boolean-Lattice Perspective for All-Loop Two-Site Cosmological Wavefunction
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.
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An Alternative Viewpoint on Kinematic Flow from Tubing Splitting
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.