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Résumé |
I will discuss the fundamentals of quantum field theory on a rigid de Sitter
space. First, I will show that the perturbative expansion of late-time
correlation functions to all orders can be equivalently generated by a non-
unitary Lagrangian on a Euclidean AdS geometry. This finding simplifies
dramatically perturbative computations, as well as allows us to establish basic
properties of these correlators, which comprise a Euclidean CFT. Second, I use
this to infer the analytic structure of the spectral density that captures the
conformal partial wave expansion of a late-time four-point function, to derive
an OPE expansion, and to constrain the operator spectrum. Third, I will prove
that unitarity of the de Sitter theory manifests itself as the positivity of the
spectral density. This statement does not rely on the use of Euclidean AdS
Lagrangians and holds non-perturbatively. |
