Towards the non-perturbative cosmological bootstrap
  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 K\"allen-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 dS$_2$.
