Cosmological correlators through the looking glass: reality, parity, and factorisation

Abstract

We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all n-point functions and allow for the exchange of additional states of any mass and integer spin. Our proof makes use of a decomposition of the inflationary bulk-bulk propagator of massive spinning fields which preserves UV-convergence and ensures that the time-ordered contributions are purely real after we rotate to Euclidean time. We use this reality property to show that the maximally-connected parts of wavefunction coefficients, from which total-energy singularities originate, are purely real. In a theory where all states are in the complementary series, this reality extends to the full wavefunction coefficient. We then use our reality theorem to show that parity-odd correlators (correlators that are mirror asymmetric) are factorised and do not diverge when the total-energy is conserved. We pay special attention to the parity-odd four-point function (trispectrum) of inflationary curvature perturbations and use our reality/factorisation theorems to show that this observable is factorised into a product of cubic diagrams thereby enabling us to derive exact shapes. We present examples of couplings between the inflaton and massive spin-1 and spin-2 fields, with the parity-violation in the trispectrum driven by Chern-Simons corrections to the spinning field two-point function, or from parity-violating cubic interactions which we build within the Effective Field Theory of Inflation. In addition, we present a first-of-its-kind example of a parity-violating trispectrum, generated at tree-level, that arises in a purely scalar theory where the inflaton mixes linearly with an additional massive scalar field.

Parity-violating scalar trispectrum from a rolling axion during inflation

“…[75][76][77][78][79][80] have measured the trispectrum of galaxy number density fields with the BOSS galaxy-clustering data and found > 3σ parity-odd signals. Measuring the CMB temperature and E-mode polarization trispecta using the Planck data has indicated weaker significance level [81,82], while it is still worth discussing the relation to new physics, and several generation mechanisms have already been proposed [74,79,80,[83][84][85][86][87].…”

“…Previous studies [74,85,87] have also computed the scalar trispectrum in other axion models where an inflaton is identified with an axion, and the axion velocity is constant in time. 1 The model of ref.…”

“…The model of ref. [87] includes a nonvanishing mass term of the gauge field, inducing different trispectrum shapes. Regarding the model of ref.…”