Building a Boostless Bootstrap for the Bispectrum
Enrico Pajer
TL;DR
The paper develops a Boostless Bootstrap framework to determine tree-level bispectra of curvature perturbations and gravitons in quasi-de Sitter spacetimes by enforcing symmetry, locality and BD vacuum at the boundary, without relying on full de Sitter boosts. It shows how to derive and constrain the graviton and scalar bispectra—⟨γγγ⟩, ⟨γζζ⟩, ⟨ζζζ⟩, and ⟨ζγγ⟩—in canonical slow-roll and EFT of inflation, including all derivative orders for scalars, while clarifying the role of soft limits and boundary terms. The approach reproduces known results (e.g. Maldacena 2002) and provides a streamlined, transparent derivation that highlights locality and vacuum choice, with a structured set of rules that can be extended to higher-point functions and to scenarios with boost-breaking dynamics. The work also discusses subtle aspects such as non-manifest locality in gravity, the interpretation of certain residues, and connections to boundary wavefunctions, pointing toward a broader program of boundary holography for cosmology and potential use of the Cosmological Optical Theorem for extending to trispectra and beyond.
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.