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Cosmological Amplitudes in Power-Law FRW Universe
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The correlators of large-scale fluctuations belong to the most important observables in modern cosmology. Recently, there have been considerable efforts in analytically understanding the cosmological correlators and the related wavefunction coefficients, which we collectively call cosmological amplitudes. In this work, we provide a set of simple rules to directly write down analytical answers for arbitrary tree-level amplitudes of conformal scalars with time-dependent interactions in power-law FRW universe. With the recently proposed family-tree decomposition method, we identify an over-complete set of multivariate hypergeometric functions, called family trees, to which all tree-level conformal scalar amplitudes can be easily reduced. Our method yields series expansions and monodromies of family trees in various kinematic limits, together with a large number of functional identities. The family trees are in a sense generalizations of polylogarithms and do reduce to polylogarithmic expressions for the cubic coupling in inflationary limit. We further show that all family trees can be decomposed into linear chains by taking shuffle products of all subfamilies, with which we find simple connection between bulk time integrals and boundary energy integrals.
Forward citations
Cited by 8 Pith papers
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Anatomy of Family Trees in Cosmological Correlators
A complete map of singularities and local series expansions for the hypergeometric building blocks of tree-level cosmological correlators.
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Geometry of Kinematic Flow
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Massive Inflationary Amplitudes: Differential Equations and Complete Solutions for General Trees
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.
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Cosmological Collider Signatures from Right-Handed Neutrino Loop
Right-handed neutrino loops in inflation with seesaw mechanism generate enhanced cosmological collider signatures via a chemical potential from a dimension-5 operator, softening Boltzmann suppression and amplifying os...
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Correlators are simpler than wavefunctions
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.
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Cosmological Correlators at the Loop Level
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.
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