Building a boostless bootstrap for the bispectrum

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 space-time. 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.

Automated summary

The study focuses on the three-point correlators of gravitons and scalar curvature perturbations around a quasi de Sitter space-time and establishes Bootstrap Rules that fully fix the form of these correlators in the asymptotic future at the boundary. The Boostless Bootstrap approach is shown to account for the breaking of de Sitter boosts caused by inflationary backgrounds. Derivations of bispectra involving gravitons in single-clock, canonical inflation are easily derived in this approach, as well as the scalar bispectrum in the Effective Field Theory of inflation to any order in derivatives. In many cases, the derivations are computationally simpler than the corresponding explicit calculations, emphasizing the implications of locality, vacuum choice, and underlying symmetries.