Towards the nonperturbative 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 latetime physics of dS$_{d+1}$, in particular on the boundary operators that appear in the latetime expansion of bulk local operators. As a first application of the Hilbert space formalism, we recover the KällenLehmann spectral decomposition of bulk twopoint 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 fourpoint 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 nonperturbative conformal bootstrap approach to the study of these latetime fourpoint functions, and we illustrate our proposal with a concrete example for QFT in dS$_2$.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.13871
 Bibcode:
 2021arXiv210713871H
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 39 pages + appendices, 3 figures