Cosmological and Fermi Scales from Hamiltonian Chaos

Abstract

A lesser-known property of Hamiltonian dynamics is that it can be formally mapped to the Riemannian geometry of classical gravitation. Taking advantage of this property, we explore here the possibility that the onset of Hamiltonian chaos in the ultraviolet (UV) sector of field theory generates the cosmological and Fermi scales. In line with the geometry of fully developed chaos, these two scales reflect the cumulative contribution of energies stored in the fractal dimensionality of spacetime. Our findings support the conjecture that both Standard and the Lambda-CDM models emerge as non-trivial attractors of the UV to infrared (IR) flow.