Faces of cosmological polytopes
Lukas Kühne
Universität Bielefeld, GermanyLeonid Monin
Swiss Federal Institute of Technology in Lausanne, Switzerland

Abstract
A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological models. More concretely, they construct a cosmological polytope for any Feynman diagram, i.e., an undirected graph. In this paper, we initiate a combinatorial study of these polytopes. We give a complete description of their faces, identify minimal faces that are not simplices and compute the number of faces in specific instances. In particular, we give a recursive description of the -vector of cosmological polytopes of trees.
Cite this article
Lukas Kühne, Leonid Monin, Faces of cosmological polytopes. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 12 (2025), no. 3, pp. 445–461
DOI 10.4171/AIHPD/192