Ising the way into de Sitter

Abstract: In statistical mechanics, the Ising model is the prototypical exactly solvable model. It is a very simple model, yet it captures a remarkable amount of physics. In this talk, will make the case that it can play a similar role for de Sitter quantum field theory and hence, for cosmology.

Concretely, I will consider the two-dimensional Ising model deformed by its thermal operator and placed on de Sitter spacetime. Although strongly interacting, the theory becomes exactly solvable through fermionisation, giving us non-perturbative access to cosmological correlators. I will present the exact thermal correlator and its late-time limit, and show how its scaling behaviour is encoded in de Sitter representation theory. I will then turn to the spin and disorder operators, which are non-local in the fermionic variables, and derive non-perturbative constraints on their late-time scaling dimensions. Finally, I will compare the exact results with conformal perturbation theory and show how late-time divergences spoil the perturbative expansion at late times, while the exact observables resum them.

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