Transition Amplitudes in de Sitter Space

TL;DR

This paper explores the dS/CFT correspondence in de Sitter space, showing how boundary correlators relate to transition amplitudes and late-time expectation values, with implications for understanding quantum gravity in cosmology.

Contribution

It provides a detailed operator formulation of the dS/CFT duality, linking bulk transition amplitudes to boundary correlators and analyzing the impact of anomalies.

Findings

Boundary correlators as transition amplitudes from Bunch-Davies vacuum

Massive bulk fields dual to two primary boundary operators

Anomalies in the dual CFT affect late-time expectation values

Abstract

Maldacena has shown that the wavefunction of the universe in de Sitter space can be viewed as the partition function of a conformal field theory. In this paper, we investigate this approach to the dS/CFT correspondence in further detail. We emphasize that massive bulk fields are dual to two primary operators on the boundary, which encode information about the two independent behaviors of bulk expectation values at late times. An operator statement of the duality is given, and it is shown that the resulting boundary correlators can be interpreted as transition amplitudes from the Bunch-Davies vacuum to an excited state in the infinite future. We also explain how these scattering amplitudes can be used to compute late-time Bunch-Davies expectation values, and comment on the effects of anomalies in the dual CFT on such expectation values.