Amplitude Bootstrap in (Anti) de Sitter Space And The Four-Point Graviton from Double Copy

Abstract: We propose studying a new representation of on-shell Anti de Sitter (AdS) amplitude in Mellin Momentum space, where it encodes all the dynamical information in Cosmological Correlators. At tree level, we demonstrate that this amplitude has a similar analytic structure as the S-matrix, with residues of poles made up of on-shell lower-point amplitudes. We use this structure to bootstrap 4-point scalar amplitudes with spin-1 and spin-2 exchange. In the second part of the paper, we use double copy to construct the 4-point graviton amplitude in general dimension. This leads us to a novel, concise formula that exhibits the flat space structure. We also verified this formula for the case when d=3 with literature.