From AdS/CFT to dS/CFT: Anomalous dimensions of bound states

The de Sitter spacetime is of fundamental importance in the field of cosmology, as it serves to model both the primordial and current expansion of the Universe. The quantum theory of inflation posits that the anisotropies of the cosmic microwave background and of the large-scale structure originate from primordial quantum fluctuations, which are imprinted in correlators at the end of inflation. A holographic correspondence between the de Sitter bulk and its conformal boundary would provide a powerful computational tool and a deeper understanding of a quantum field theory embedded in de Sitter space. Nevertheless, while numerous useful results in the context of AdS/CFT have already been obtained, the dS case presents a distinctive behaviour due to the conformal boundary being a spacelike hypersurface at time infinity, which gives rise to an Euclidean dual CFT. One may circumvent this problem by exploiting a map between Schwinger-Keldysh boundary propagators in dS and those in Euclidean AdS. These are linked by an analytical continuation, which becomes a simple phase shift in the Mellin-Barnes representation. From this relation, it is possible to express Schwinger-Keldysh diagrams in dS at all orders in perturbation theory as a sum of Witten diagrams in EAdS. By utilising the EAdS spacetime as an intermediary, a perturbative dS/CFT correspondence can be constructed. Following the presentation of these core results, the thesis will proceed to present an original computation achieved via the aforementioned holographic approach. The objective is to compute the anomalous dimensions of double-trace operators of the boundary CFT, which are associated with exchanges of bound states in the bulk. This boundary quantity is a means of encoding information on the stability of bound states and their mass spectrum. It will be demonstrated that even such dS anomalous dimensions can be expressed in terms of the related anomalous dimensions in the EAdS.