From on-shell amplitude in AdS to cosmological correlators: gluons and gravitons

We recently introduced a recursive bootstrap method for constructing $n$-point gluon and graviton Mellin-momentum amplitudes in (A)dS spacetime. The power of this approach was illustrated by our successful computation of the first five-point graviton amplitude in (A)dS. In this work, we provide further details of these calculations and start with a more in-depth review of the formalism by offering detailed insights into the motivation for defining on-shell amplitudes in AdS, along with various explicit examples. Furthermore, we demonstrate how cosmological correlators can be effortlessly obtained once the amplitude is determined.