Leading loops in cosmological correlators

Abstract

Cosmological correlators from inflation are often generated at tree level and hence loop contributions are bounded to be small corrections by perturbativity. Here we discuss a scenario where this is not the case. Recently, it has been shown that for any number of scalar fields of any mass, the parity-odd trispectrum of a massless scalar must vanish in the limit of exact scale invariance due to unitarity and the choice of initial state. By carefully handling UV-divergences, we show that the one-loop contribution is non-vanishing and hence leading. Surprisingly, the one-loop parity-odd trispectrum is simply a rational function of kinematics, which we compute explicitly in a series of models, including single-clock inflation. Although the loop contribution is the leading term in the parity-odd sector, its signal-to-noise ratio is typically bounded from above by that of a corresponding tree-level parity-even trispectrum, unless instrumental noise and systematics for the two observables differ. Furthermore, we identify a series of loop contributions to the wavefunction that cancel exactly when computing correlators, suggesting a more general phenomenon.

The cosmological tree theorem

“…ψ 1-loop 2 , ψ tree 4 and ψ tree 3 × ψ tree 3 in the power spectrum. This generalises some of the important observations made recently in [31] about which wavefunction singularities can appear in correlators.…”

“…16 In the wavefunction coefficients, such vertices generically do appear and lead to branch cuts in the total external energy once the loop integration is performed. These branch cuts do not appear in equal-time correlators, as noted in [31,127] in various examples, and our tree theorem makes their cancellation manifest. We demonstrate that this cancellation is not confined to the power spectrum or bispectrum, but in fact takes place very generally.…”

“…In the analogous calculation of the inclusive cross-section, this cancellation is the so-called KLN theorem. The fact that in-in correlators enjoy a "cosmological KLN theorem", thanks to causality and the tree theorem (2.60), explains why several recent calculations of equal-time correlation functions have found a simpler analytic structure than the corresponding wavefunction coefficients [31,127].…”

“…On a cosmological (time-dependent) spacetime background, things are even worse: loop diagrams contain potentially divergent integrals both over momenta and over time. Since loop corrections can JHEP12(2023)076 play an important role in a wide variety of cosmological settings -including precise calculations of the primordial power spectrum [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and non-Gaussianity [19][20][21][22][23][24][25][26][27][28][29][30][31]; inflationary features that may seed primordial black holes [32][33][34][35][36][37][38][39][40][41] or produce a stochastic gravitational wave background [42][43][44][45][46]; de Sitter holography …”

Nonanalyticity and on-shell factorization of inflation correlators at all loop orders

“…The analytic property of dS amplitudes was much less explored than their flat-space counterparts, but this direction has attracted lots of attentions recently. New results include various bootstrap methods using a variety of basic physical principles as input [68][69][70][71][72][73][74][75][76][77][78], the study of unitarity, causality, symmetries, and their implications to analytical structures [79][80][81][82][83][84][85][86], the Mellin-space approach to dS amplitudes [87][88][89][90][91][92], the study of analytical structure and explicit results using techniques of partial Mellin-Barnes (MB) representation [51,[93][94][95], spectral decomposition [96,97], and new results for spinning fields [98][99][100][101] and parity violations [60,[102][103][104]. There are other approaches to explore the analytical structure of dS amplitudes, including the cosmological polytopes [105,106], the scattering equation [107,108].…”