Interacting Dirac fields in an expanding universe: dynamical condensates and particle production

Abstract: The phenomenon of particle production for quantum field theories in curved spacetimes is crucial to understand the large-scale structure of a universe from an inflationary epoch. In contrast to the free and fixed-background case, the production of particles with strong interactions and back reaction is not completely understood, especially in situations that require going beyond perturbation theory. In this work, we present advances in this direction by focusing on a self-interacting field theory of Dirac fermions in an expanding Friedmann-Robertson-Walker universe. By using a Hamiltonian lattice regularization with continuous conformal time and rescaled fields, this model becomes amenable to either a cold-atom analogue-gravity quantum simulation, or a dynamical variational approach. Leveraging a family of variational fermionic Gaussian states, we investigate how dynamical mass generation and the formation of fermion condensates associated to certain broken symmetries modify some well-known results of the free field theory. In particular, we study how the non-perturbative condensates arise and, more importantly, how their real-time evolution has an impact on particle production. Depending on the Hubble expansion rate, we find an interesting interplay of interactions and particle production, including a non-trivial back reaction on the condensates and a parity-breaking spectrum of produced particles.