From Amplitudes to Contact Cosmological Correlators

TL;DR

This work develops a boostless cosmological bootstrap by constructing a contact reconstruction formula that turns tree-level, local $n$-point amplitudes into de Sitter wavefunction coefficients, enabling the all-orders derivation of scalar four-point trispectra from boost-breaking interactions. It uses Hilbert-series methods to enumerate four-point amplitudes, identifies primary and secondary generators, and computes explicit trispectrum shapes within the EFT of inflation, while clarifying how the flat-space amplitude informs de Sitter physics. The approach is extended to higher-point functions, with a systematic counting of amplitudes and wavefunction coefficients, and a detailed comparison between reconstruction and bulk-time integrals is provided. The results broaden the boostless cosmological bootstrap, establishing a practical framework to generate and classify primordial non-Gaussianity shapes and linking flat-space scattering data to cosmological observables.

Abstract

Our understanding of quantum correlators in cosmological spacetimes, including those that we can observe in cosmological surveys, has improved qualitatively in the past few years. Now we know many constraints that these objects must satisfy as consequences of general physical principles, such as symmetries, unitarity and locality. Using this new understanding, we derive the most general scalar four-point correlator, i.e., the trispectrum, to all orders in derivatives for manifestly local contact interactions. To obtain this result we use techniques from commutative algebra to write down all possible scalar four-particle amplitudes without assuming invariance under Lorentz boosts. We then input these amplitudes into a contact reconstruction formula that generates a contact cosmological correlator in de Sitter spacetime from a contact scalar or graviton amplitude. We also show how the same procedure can be used to derive higher-point contact cosmological correlators. Our results further extend the reach of the boostless cosmological bootstrap and build a new connection between flat and curved spacetime physics.