From dS to AdS and back

We describe in more detail the general relation uncovered our previous work between boundary correlators de Sitter (dS) and Euclidean anti-de (EAdS) space, at any order perturbation theory. Assuming Bunch-Davies vacuum early times, given diagram contributing to a correlator dS can be expressed as linear combination of Witten diagrams for corresponding process EAdS, where relative coefficients are fixed by consistent on-shell factorisation dS. These certain sinusoidal factors which account change coefficient contact sub-diagrams from EAdS dS, we argue encode (perturbative) unitary time evolution with initial conditions thus perturbatively have same singularity structure their AdS counterparts identities them allow directly import wealth techniques, results understanding This includes Conformal Partial Wave expansion and, going single-valued Lorentzian AdS, Froissart-Gribov inversion formula. give few (among many possible) applications both tree loop level. Such made manifest Mellin-Barnes representation correlators, point out is useful tool its own right analogue Fourier transform dilatation group. The particular makes dispersion formulas bulk-to-bulk propagators (EA)dS, imply Cutkosky cutting rules (EA)dS. Our completely apply interaction (integer) spinning fields.