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

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