On-shell Bootstrap for n-gluons and gravitons scattering in (A)dS, Unitarity and Soft limit

We propose an algorithm to recursively bootstrap $n$-point gluon and graviton Mellin-Momentum amplitudes in (A)dS spacetime using only three-point amplitude. We discover that gluon amplitudes are simply determined by factorization for $n\ge 5$. The same principle applies to $n$-point graviton amplitudes, but additional constraints such as flat space and soft limits are needed to fix contact terms. Furthermore, we establish a mapping from $n$-point Mellin-Momentum amplitudes to $n$-point cosmological correlators. We efficiently compute explicit examples up to five points. This leads to the first five-graviton amplitude in $Ad{S}_{d+1}$.