Cosmological Correlators Through the Looking Glass: Reality, Parity, and Factorisation

TL;DR

This paper proves that total-energy singularities in inflationary wavefunctions are purely real under certain conditions, and uses this to show that parity-odd correlators are factorised and finite, with applications to inflationary models involving massive spinning fields.

Contribution

It establishes a reality theorem for inflationary wavefunctions and demonstrates the factorisation and finiteness of parity-odd correlators, including the trispectrum, with new insights into inflationary couplings.

Findings

Total-energy singularities are purely real for massless scalars and gravitons.

Parity-odd correlators are factorised and finite at total-energy conservation.

Explicit examples of parity-violating couplings in inflationary models are provided.

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.