Building a Boostless Bootstrap for the Bispectrum

TL;DR

This paper develops a bootstrap approach to determine primordial three-point correlators in cosmology, accounting for broken de Sitter boosts, simplifying calculations, and providing new results for scalar bispectra in inflation.

Contribution

It introduces a Boostless Bootstrap method that fully constrains primordial correlators at the boundary without bulk evolution, including new scalar bispectrum results in EFT of inflation.

Findings

Bootstrap rules fix correlators without bulk evolution.

Derived scalar bispectrum in EFT of inflation to all derivative orders.

Simplified derivations highlight locality, vacuum choice, and symmetries.

Abstract

The observation of primordial correlators by cosmological surveys is a very promising avenue to probe high energies and the perturbative regime of quantum gravity. Hence, it is imperative that we understand how these observables are shaped by the pillars of fundamental physics, namely unitarity, locality and symmetries. To this end, we study the three-point correlators of gravitons and scalar curvature perturbations around a quasi de Sitter spacetime. We identify a set of Bootstrap Rules that fully fix the form of these correlators in the asymptotic future, i.e. at the boundary, and make no reference to bulk time evolution. Importantly, our Boostless Bootstrap accounts for the ubiquitous (spontaneous) breaking of de Sitter boosts caused by any inflationary background. We show how all bispectra involving gravitons in single-clock, canonical inflation can be easily derived in this approach. We also derive for the first time the scalar bispectrum in the Effective Field Theory of inflation to any order in derivatives. In many cases, our derivation is computationally simpler than the corresponding explicit calculation, and makes particularly transparent the implications of locality, the choice of vacuum, and the underlying symmetries.