It is a bold idea: what if the same mathematical structures could describe both collisions in particle accelerators and the formation of the universe? Positive geometry, based on geometric objects with well-defined volumes in high-dimensional spaces, is reshaping a field traditionally dominated by Feynman diagrams. Among these objects is the amplituhedron, introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka.
At the heart of this approach lies the idea that quantum interactions can be represented as volumes. This geometric language offers a fresh perspective that could make it possible to better unify "the very small," studied in particle physics, and "the very large," explored in cosmology.
