Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue

When gravitation is introduced in Quantum Field Theory, even at a semi-classical level, there is a plethora of surprising phenomena that arise. One of the most relevant is particle production due to the dynamics of an expanding universe. We propose a cold-atom gravitational analogue as a platform for the study of this phenomenon. We begin by exploring the formalism describing fermion production in a (1+1)-dimensional de Sitter spacetime and show some relevant results. After this, and as a first step towards its implementation in a quantum simulator, we consider two possible lattice regularizations, which allow us to explore the interplay of particle production and topological phenomena in spacetimes with a boundary. In particular, we show that for a Wilson-type discretization of the Dirac field, the asymptotic Minkowski vacua connected by an intermediate expansion correspond to symmetry-protected topological groundstates, and have a boundary manifestation in the form of zero-modes exponentially localised to the spatial boundaries. This allows one to explore the interaction between them and the expanding background. We then present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices, which would allow for the exploration of new domains in QFT in curved spacetimes, such as interacting theories, in the future.