Cosmohedra

In this talk, I will discuss Cosmohedra. These are geometric objects which encode the vacuum wavefunction for theories with colored scalars with cubic interactions. I will start by introducing the vacuum wavefunction, both in Minkowski and de Sitter spacetime, and its fundamental properties. As well as, a new kinematic parameterization in terms of sub-polygons of the momentum polygon. Then, I will review the ABHY associahedron, the geometry underlying scattering amplitudes of colored scalars with cubic interactions. Finally, I will discuss how to construct the Cosmohedron by “blowing up” the faces of the Associahedron. And will provide a concrete definition of this class of polytopes, as well as a way to compute the wavefunction. I will also discuss the extension of this geometry to n-point correlation functions.