Towards the non-perturbative cosmological bootstrap

Abstract

We study Quantum Field Theory (QFT) on a background de Sitter spacetime dS d+1 . Our main tool is the Hilbert space decomposition in irreducible unitarity representations of its isometry group SO(d + 1, 1). Throughout this work, we focus on the late-time physics of dS d+1 , in particular on the boundary operators that appear in the late-time expansion of bulk local operators. As a first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of bulk two-point functions. In the process, we exhibit a relation between poles in the corresponding spectral densities and boundary CFT data. Next, we study the conformal partial wave decomposition of four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity properties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in dS2.

Exceptional scalar theories in de Sitter space

“…This is the purview of the cosmological bootstrap, which aims to classify the space of possible cosmological correlators, and so constrain the physics of inflation (see, e.g., Refs. [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] for recent developments). It is natural to wonder about the role of these scalar theories in the bootstrap construction: how precisely are their special properties reflected in their (A)dS correlators?…”

Spinors and conformal correlators

“…Finally, the last area in which this work can have an impact is quantum field theory in de Sitter space-time. Many recent works have exploited the Euclidean conformal symmetry of late-time correlators [47][48][49][50][51][52], but the Lorentzian conformal group also plays an important role in the in-in formalism recently put forward [53][54][55][56].…”

Physical Representations for Scattering Amplitudes and the Wavefunction of the Universe

“…In cosmology, the understanding of relevant quantum mechanical observables, such as the spatial correlations and the wavefunction of the universe, as well as the physics they encode and the technology to compute them, are all significantly more primitive. The way that fundamental physical principles, such as unitarity and causality, reflect into and constrain these observables, started to be elucidated only recently, via the proof of a cosmological optical theorem [27] and the associated cutting rules [28][29][30][31], the positivity of the spectral den-sity [32,33], as well as the proof of existence Steinmannlike relations [34].…”

“…. (32) It is interesting to notice that for any graph G, one of the sets of subgraphs completely marking G and such that its elements introduce complementary markings, is constituted by the graph G and all the subgraphs g s containing a single site s. They identify a codimension-(n s + 1) subspace of the locus C of the intersections of the facets of P G outside P G . Hence, expression (32) for the canonical form considering G…”