From the flat-space S-matrix to the Wavefunction of the Universe

The physical information encoded in the cosmological late-time wavefunction of the universe is tied to its singularity structure and its behaviour as such singularities are approached. One important singularity is identified by the vanishing of the total energy, where the wavefunction reduces to the physics of scattering in flat space. In this paper, we discuss the behaviour of the perturbative wavefunction as its other singularities are approached and the role played by the flat-space scattering, in the simplified context of the class of toy models admitting a first principle definition in terms of cosmological polytopes. The problems then translates into the analysis of the structure of its facets, one of which -- the scattering facet -- beautifully encodes the flat-space S-matrix. We show that all the boundaries of the cosmological polytope encode information about the flat-space physics. In particular, a subset of its facets turns out to have a similar structure as the scattering facet, with the vertices which can be grouped together to form lower dimensional scattering facets. The other facets admit one (and only one) triangulation in terms of products of lower dimensional scattering facets. As a consequence, the whole perturbative wavefunction can be represented as a sum of product of flat-space scattering amplitudes. Finally, we turn the table around and ask whether the knowledge of the flat-space scattering amplitudes suffices to reconstruct the wavefunction of the universe. We show that, at least for our class of toy models, this is indeed the case at tree level if we are also provided with a subset of symmetries that the wavefunction ought to satisfy. Once the tree cosmological polytopes are reconstructed, the loop ones can be obtained as a particular projection of them.