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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Qin and Z.-Z
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abstract
Massive spinning particles acquire helicity-dependent chemical potentials during the inflation from axion-type couplings. Such spinning fields can mediate sizable inflaton correlators which we call the helical inflation correlators. Helical inflaton correlators are approximately scale invariant, dS boost breaking, parity-violating, and are promising observables of cosmological collider physics. In this work, we present complete and analytical results for 4-point helical inflation correlators with tree-level exchanges of massive spinning particles, including both the smooth background and the oscillatory signals. We compute the bulk Schwinger-Keldysh integrals in two independent ways, including the partial Mellin-Barnes representation and solving bootstrap equations. We also present new closed-form analytical results for 3-point functions with massive scalar or helical spinning exchanges. The analytical results allow us to concretely and efficiently explore the phenomenological consequences of helicity-dependent chemical potentials. In particular, we show that the chemical potential can exponentially enhance oscillatory signals of both local and nonlocal types, but only affects the background in a rather mild way. Our results extend the de Sitter bootstrap program to include nonperturbative breaking of de Sitter boosts. Our results also explicitly verify the recently proposed cutting rule for cosmological collider signals.
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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.
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.
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.
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.
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.
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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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
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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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Laplace Space for Cosmological Correlators
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.
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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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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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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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Cosmological Collider Signatures from Right-Handed Neutrino Loop
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.
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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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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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