Abstract
We study the fundamentals of quantum field theory on a rigid de Sitter space. We 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. We 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. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, 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. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one- loop-resummed exchange diagrams. An exchanged particle appears as a resonant feature in the spectral density which can be potentially useful in experimental searches.
Highlights
De Sitter space is the most symmetric and in this sense the simplest cosmological spacetime
We 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 anti-de Sitter (AdS) geometry
We develop a systematic framework to reduce any perturbative calculation in De Sitter (dS) to that in Euclidean AdS (EAdS), where plentiful computational techniques have been developed
Summary
De Sitter (dS) space is the most symmetric and in this sense the simplest cosmological spacetime. Some large N quantum field theories on a rigid dS background are known to be holographically dual to a gravitational spacetime that includes a FRW-like geometry with a crunching singularity, see the appendix of [4], as well as [5–11] for concrete examples in string theory. This connection to cosmology is less direct than what was discussed above, but it would allow us to study quantum gravity in a cosmological setup using tools of quantum field theory on a rigid dS, which we develop in this paper.
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