We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar ϕ4-theory in Euclidean AdS4, by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams.

We consider the semi-classical expansion of the Bunch-Davies wavefunction with future boundary condition in position space for a real scalar field, conformally coupled to a classical de Sitter background in the expanding Poincaré patch with quartic selfinteraction. In the future boundary limit the wave function takes the form of the generating functional of a Euclidean conformal field theory for which we calculate the anomalous dimensions of the double trace deformations at one loop order using results obtained from Euclidean Anti de Sitter space. We find analytic expressions for some subleading twist operators and an algorithm to obtain expressions for general twist.

We perform an off-shell treatment of asymptotically decelerating spatially flat FRW spacetimes at future null infinity. We obtain supertranslation and superrotation-like asymptotic diffeomorphisms which are consistent with the global symmetries of FRW and we compute how the asymptotic data is transformed under them. Further, we study in detail the effect of these diffeomorphisms on some simple backgrounds including unperturbed FRW and Sultana-Dyer black hole. In particular, we investigate how these transformations act on several cosmologically perturbed backgrounds.

In this paper, we extend the treatment of asymptotically decelerating spatially flat FLRW spacetimes initiated in [1]. We show that a certain class of those metrics is ruled by the asymptotic algebra bms s , which belongs to a one-parameter family of deformations of bms. Furthermore, we enlarge our ansatz to include Diff(S 2 ) transformations whose asymptotic algebra gbms s is a one parameter deformation of gbms. Therefore, the holographic algebras bms s and gbms s in FLRW can be related to their flat counterparts through a cosmological holographic flow. Finally, we introduce a logarithmic ansatz in order to account for cosmological black holes, which does not generally satisfy the peeling property but preserves the asymptotic algebra.

Using the Schwinger-Keldysh-formalism, reformulated in [1] as an effective field theory in Euclidean anti-de Sitter, we evaluate the one-loop cosmological four-point function of a conformally coupled interacting scalar field in de Sitter. Recasting the Witten cosmological correlator as flat space Feynman integrals, we evaluate the one-loop cosmological four-point functions in de Sitter space in terms of single-valued multiple polylogarithms. From it we derive anomalous dimensions and OPE coefficients of the dual conformal field theory at space-like, future infinity. In particular, we find an interesting degeneracy in the anomalous dimensions relating operators of neighboring spins.