Harry Goodhew and Gordon Lee talk about their recent work on “cosmological correlators”.

Observationally these would be power spectra, bispectra, etc; however on the theory side they find it easier to work with pieces of the “wavefunction of the universe”, which are closely related to observational correlation functions.

They show constraints on the form these correlators can take that arise from imposing unitarity during inflation. Contrary to prior expectations these constraints apply not just in space-times that are exactly de Sitter, but in fact in any flat FLRW space-time.

The most relevant paper: https://arxiv.org/abs/2104.06587

Harry: https://www.maths.cam.ac.uk/person/hfg23
Gordon: https://www.damtp.cam.ac.uk/person/mhgl2