### Abstract

We shall start from the role of KMS states in two different contexts, first in arithmetic then in the electroweak phase transition in particle physics. We shall then build a dictionary between the set-up of noncommutative geometry leading to the spectral realization of the zeros of the Riemann zeta function and a tentative set-up to encode the spectral model in Lorentzian signature, allowing to relate to cosmological models. This is joint work with Matilde Marcolli.