Aspects of Gravitational and Cosmological Scattering Amplitudes

Abstract

This thesis presents three distinct aspects of scattering amplitudes research along with background material on the concepts underpinning them. The first of these is the study of on-shell diagrams for supergravity and an associated recursion relation automatically encorporating the bonus relations. This is used to produce momentum twistor expressions which in the case of six-point NMHV use different `coordinate patches' with different ordering of external legs to get compact results and see the cancellation of spurious poles through momentum twistors. The second is the study of colour/kinematics duality of Yang-Mills amplitudes in four-dimensional Anti-de Sitter (AdS) space. By applying a generalised gauge transformation the kinematic numerators can be made to obey a Jacobi relation and these shifted numerators also obey a deformed AdS version of the Bern-Carrasco-Johansson relations. Finally we study wavefunction coefficients of scalar effective field theories (EFTs) in de Sitter space using a representation involving boundary conformal generators acting on contact diagrams and the cosmological scattering equations. Through this representation,
we show that four-point wavefunction coefficients of EFTs exhibit double copy relations analogous to those in flat space with additional curvature corrections with unfixed coefficients. Imposing enhanced soft limits analogous to the EFTs in flat space allows these to be unambiguously fixed and also recovers Lagrangians with hidden shift symmetries. This is explored at four- and six-point.