A Match Made in Heaven: Linking Observables in Inflationary Cosmology

TL;DR

This paper demonstrates that in parity-odd inflationary models, certain higher-order correlation functions like the trispectrum can be expressed in terms of lower-order correlators, revealing a factorization property.

Contribution

It shows that in dynamical Chern-Simons gravity, the parity-odd trispectrum can be derived solely from the bispectrum and power spectrum, illustrating a new factorization in inflationary correlators.

Findings

Parity-odd trispectrum expressed in terms of bispectrum and power spectrum.

The trispectrum is quadratic in the mixed inflaton-graviton bispectrum.

The derived trispectrum is a simple, rational, factorized function of momenta.

Abstract

Cosmological correlation functions of inflaton and graviton perturbations are the fundamental observables of early universe cosmology and remain a primary target for observations. In this work, we ask the following question: are these observables independent of one another? We find that in the parity-odd sector of inflationary perturbation theory, the answer is a resounding no! In earlier work we derived a correlator-to-correlator factorisation formula which states that parity-odd correlators factorise into lower-point correlators under some mild assumptions on the underlying theory. In this work, we show that these assumptions are satisfied in dynamical Chern-Simons gravity where the action of minimal inflation is augmented by a coupling between the inflaton and the gravitational Chern-Simons term. Such a theory gives rise to a parity-odd trispectrum of curvature perturbations, and we show that such a trispectrum can be expressed solely in terms of the bispectrum that arises due to the minimal coupling between the inflaton and graviton, and the graviton power spectrum which receives a parity-odd correction in this theory. The trispectrum is quadratic in this mixed inflaton-graviton bispectrum and can therefore be interpreted as a ``double copy". Our final expression for the parity-odd trispectrum is a relatively simple function of the external momenta that is rational and factorised.