IAS Amplitudes Group Meeting

Abstract: Is there a geometric object underlying the cosmological wavefunction for Tr $\phi^3$ theory, just as associahedra underlie scattering amplitudes? In this talk, I will describe a new class of polytopes that answer this question. I will start by reviewing the perturbative computation of the wavefunction and explain how it is organized in terms of collections of non-overlapping subpolygons living inside the momentum polygon. This combinatorial information is much richer than that of Tr $\phi^3$ amplitudes, where the diagrams correspond to triangulations of the same polygon. Nonetheless, as I will show the geometric descriptions are closely related — the polytopes for cosmology are obtained by "blowing up" the faces of the associahedron in a natural way. I will give a concrete definition of this class of polytopes, show how they work in some simple examples, and describe a number of open questions about the physics and mathematics associated with them.