A Laplace-space representation converts massive single-exchange cosmological correlators in de Sitter into a rapidly convergent series derived from flat-space integrals.
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The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
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abstract
We extend the cosmological bootstrap to correlators involving massless particles with spin. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three- and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.
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A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
Derives integro-differential boundary equations from bulk locality for scale-breaking cosmological correlators with oscillating heavy-field masses and solves them analytically and numerically to reveal enhanced collider signals.
The double-exchange cosmological correlator is computed in KLF space, yielding a double series over hypergeometric functions that improves on prior four-layer representations.
Laplace transform converts cosmological correlator diagrams into flat-space integrals against kernels, yielding a closed-form rapidly convergent series for the massive single-exchange case valid across the full kinematic domain.
Tree-level gluon correlators in AdS4 decompose into energy poles with residues given by flat-space amplitudes, curvature corrections captured by lower-point amplitudes with merged data via AdS Berends-Giele currents.
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.
A new symplectic bi-Grassmannian representation encodes CFT4 Wightman correlators via integrals over mutually symplectically orthogonal n-planes aligned with kinematics, reproducing known 2- and 3-point structures compactly and revealing double-copy properties.
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 new Super-Grassmannian integral formalism for N=1 SCFT3 correlators enforces symmetries manifestly and relates all component functions to one, enabling construction of AdS4 gluon correlators from gluino ones.
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.
Standard SdSET power counting fails for classically conformal φ⁴; leading superhorizon modes must be read from the two-loop anomalous dimension of the two-point function.
Tree-level Yang-Mills de Sitter wavefunctions through six points are reconstructed from cosmological cuts into cut-detectable gluings plus a current-conservation completion, matching Feynman rules and suggesting an all-n scalar-tubing structure.
Chemical potential from a unique dim-5 inflaton–right-handed-neutrino operator softens heavy-mass Boltzmann suppression and amplifies helicity-dependent oscillatory non-Gaussianity from the fermion triangle loop.
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.
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.
Tree-level N=2 super wavefunction coefficients are written in orthogonal-Grassmannian form by inverting a basis of energy discontinuities and embedding them in momentum superspace.
The equilateral bispectrum from massive scalar exchange in inflation is not universally negative in the full EFT of inflation; its sign depends on a critical ratio of operator coefficients.
Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.
A new Super-Grassmannian organizes SCFT3 correlators with manifest symmetries and connects AdS4 results to N=4 SYM amplitudes in the flat-space limit.
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.
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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.