QFT in nearly dS space-times and, more generally, in FRW backgrounds allows us to describe correlations at the end of inflation. However, how to extract fundamental physics out of them is still a challange: we do not even know how fundamental pillars such as causality and unitarity of the time evolution constrain them. In this talk I will present a recent program which aims to construct the wavefunction of the universe, which generates these correlations, directly from first principles without making any reference to time evolution: these observables naturally live at the boundary of the nearly dS/FRW space-times and the time evolution is integrated out. I will discuss two approaches: one approach aims to construct the wavefunction from the knowledge of its general analytic properties, in a similar fashion as scattering amplitudes in flat space-time (which can be formulated directly from on-shell data with no reference to fields whatsoever); the second approach aims to find new mathematical objects, with their own first principle definition, which has the very same properties we ascribe to the wavefunction of the universe, with all the basic physical principles such as causality and unitarity, emerging from their intrinsic definition.
Paolo Benincasa: Towards a reformulation of QFT in expanding universes