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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Boostless cosmological collider bootstrap
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abstract
Cosmological correlation functions contain valuable information about the primordial Universe, with possible signatures of new massive particles at very high energies. Recent developments, including the cosmological bootstrap, bring new perspectives and powerful tools to study these observables. In this paper, we systematically classify inflationary three-point correlators of scalar perturbations using the bootstrap method. For the first time, we derive a complete set of single-exchange cosmological collider bispectra with new shapes and potentially detectable signals. Specifically, we focus on the primordial scalar bispectra generated from the exchange of massive particles with all possible boost-breaking interactions during inflation. We introduce three-point "seed" functions, from which we bootstrap the inflationary bispectra of scalar and spinning exchanges using weight-shifting and spin-raising operators. The computation of the seed function requires solving an ordinary differential equation in comoving momenta, a boundary version of the equation of motion satisfied by a propagator that linearly mixes a massive particle with the external light scalars. The resulting correlators are presented in analytic form, for any kinematics. These shapes are of interest for near-future cosmological surveys, as the primordial non-Gaussianity in boost-breaking theories can be large. We also identify new features in these shapes, which are phenomenologically distinct from the de Sitter invariant cases. For example, the oscillatory shapes around the squeezed limit have different phases. Furthermore, when the massive particle has much lower speed of sound than the inflaton, oscillatory features appear around the equilateral configuration.
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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.
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.
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 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.
Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized interactions.
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.
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.
Unified tree-level bispectrum shapes for cosmological collider processes are computed and searched in Planck data, yielding no detection but a weak hint for chemical potential extensions at ω - M ≃ 3H.
In a string-inspired two-field axion monodromy model, oscillatory modulations excite heavy moduli during inflation, producing detectable cosmological collider signals in the primordial bispectrum that bypass Boltzmann suppression.
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.
citing papers explorer
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Massive Cosmological Correlators from Flat Space: a Laplace-Space Approach
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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Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
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.
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Every Wrinkle Carries A Memory: An Integro-differential Bootstrap for Features in Cosmological Correlators
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.
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Cosmological Correlators in KLF and the Double-Exchange
The double-exchange cosmological correlator is computed in KLF space, yielding a double series over hypergeometric functions that improves on prior four-layer representations.
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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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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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Differential Equations for Massive Correlators
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
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Strongly Coupled Sectors in Inflation: Gapped Theories of Unparticles
Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized interactions.
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Strongly Coupled Sectors in Inflation: Gapless Theories and Unparticles
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.
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On Cosmological Correlators with Boundary Contributions
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.
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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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Scalars at the Cosmological Collider: Full Shapes of Tree Diagrams and Bispectrum Searches using Planck Data
Unified tree-level bispectrum shapes for cosmological collider processes are computed and searched in Planck data, yielding no detection but a weak hint for chemical potential extensions at ω - M ≃ 3H.
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The UV Sensitivity of Axion Monodromy Inflation
In a string-inspired two-field axion monodromy model, oscillatory modulations excite heavy moduli during inflation, producing detectable cosmological collider signals in the primordial bispectrum that bypass Boltzmann suppression.
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A Match Made in Heaven: Linking Observables in Inflationary Cosmology
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.
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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.
- Non-Relativistic Cosmological Collider Signals