Abstract

Our understanding of physical phenomena is intimately linked to the way we understand the relevant observables describing them. While a big deal of progress has been made for processes occurring in flat space-time, much less is known in cosmological settings, where it is still unclear how to isolate fundamental physics from the relevant observables: we do not know how to answer the question “what are the conditions they ought to satisfy in order to come from a consistent evolution in cosmological space-times?”. In this talk I will illustrate the path my collaborators and I have recently undertaken in order to address such a question, aiming towards the idea of a formulation of cosmology “without time”.

The focus of the discussion will be the late-time wavefunction of the universe for a large class of scalar toy models and its properties in perturbation theory. I will discuss its singularity structure and how it satisfies a recursion relation, which allows to compute it directly in terms of “boundary” data. Amazingly enough, a new mathematical structure, we called “cosmological polytopes”, which has its own first principle definition, encodes the singularity structure we ascribe to the perturbative wavefunction of the universe, and makes explicit its relation to the flat-space S-matrix. After a gentle introduction to the cosmological polytopes, I will stress how they allow us to: compute the wavefunction of the universe at arbitrary points and arbitrary loops (with novel representations for it); interpret the residues of its poles in terms of flat-space processes; provide a general geometrical proof for the flat-space cutting rules; reconstruct the perturbative wavefunction from the knowledge of the flat-space S-matrix and a subset of symmetries enjoyed by the wavefunction.