Cosmological correlators in gravitationally-constrained de Sitter states

TL;DR

This paper investigates cosmological correlators in de Sitter quantum gravity at vanishing Newton's constant, highlighting how gravitational constraints influence observable invariance and the emergence of QFT-like correlators in specific states.

Contribution

It introduces a framework for computing de Sitter correlators in quantum gravity, formulates Feynman rules, and distinguishes between invariant and QFT-like observables in different states.

Findings

Correlators are conformally invariant in allowed states.

Sample computations show non-Gaussianities even with Gaussian vacua.

State-dependent observables can approximate QFT correlators in certain backgrounds.

Abstract

We study cosmological correlators in de Sitter quantum gravity in the limit where $G_N \to 0$. This limit is distinct from a nongravitational QFT because the gravitational constraints still force states and observables to be de Sitter invariant. We first examine a class of perturbative correlators that, in gauge-fixed form, are represented by the expectation value of a product of elementary fields on the late-time boundary. We formulate Feynman rules for our computations and enumerate some necessary, but not sufficient, conditions that must be imposed on states and operators to avoid group-volume divergences. These correlators are conformally invariant in all allowed perturbative states but never coincide with QFT vacuum-expectation values. For instance, our sample computations yield interesting non-Gaussianities even when the underlying vacuum wavefunction is Gaussian. However, we show that, in the presence of a heavy background state, it is possible to construct a separate class of state-dependent relational observables whose values approximate QFT correlators in the vacuum. This illustrates a key contrast in quantum gravity -- between observables that are microscopically simple and observables whose expectation values in an appropriate background state lead to simple QFT-like correlators.