From Amplitude Bootstrap to Cosmological Correlators

In this thesis, we explore how to adapt the amplitude bootstrap techniques from Minkowski space to (Anti) de-Sitter space. We begin by reviewing the use of physical principles to bootstrap amplitudes in flat spacetime. Building on this foundation, the first part of the thesis examines the relationship between enhanced soft limits and effective field theories in de-Sitter space. Specifically, we analyze the soft limits of theories with Lagrangians that exhibit hidden shift symmetries, demonstrating that these theories indeed possess enhanced soft limits up to six points. In the second part, we focus on spinning particles. Starting with the four-point gluon wavefunction coefficient, we use the double copy idea by squaring the gluon result. Then, by combining this with the bootstrap techniques, we compute the four-graviton wavefunction coefficient in de-Sitter space. In the final part of the thesis, we investigate the Mellin-Momentum representation of AdS amplitudes. This representation, which resembles the analytic structure of the S-matrix, enables us to introduce a novel and efficient algorithm for bootstrapping n-point amplitudes, incorporating the modern on-shell amplitude approach. We then compute gluon and gravity amplitudes up to five points.