GFiRe: a Gauge Field integrator for Reheating

TL;DR

This paper introduces GFiRe, a new numerical algorithm and code for accurately simulating the non-linear evolution of gauge and scalar fields during cosmic reheating, ensuring exact Gauss constraint preservation and energy conservation.

Contribution

GFiRe is the first code to combine lattice gauge techniques with symplectic integrators that exactly preserve the Gauss constraint in expanding universe simulations.

Findings

Energy conservation violation less than 10^{-4}

Gauss constraint violation less than 10^{-6}

Successfully simulates complex reheating dynamics

Abstract

We present a new numerical algorithm and code, ${\sf GFiRe}$, for solving the non-linear evolution of Abelian gauge fields coupled to complex scalar fields in homogeneous and isotropic spacetimes. We adopt a hybrid approach to solving the system: the spatial derivatives are discretized using standard Lattice Gauge Field Theory techniques, whereas the time evolution of the fields and scale factor is implemented with explicit, composite, symplectic integrators. An important property of our compound algorithm is that the discretized Gauss constraint is respected exactly, regardless of the order of the symplectic integrator. This remains true even when the background expansion is computed "self-consistently"; that is, when the expansion history is computed using spatial averaged components of the energy momentum tensor in the simulation volume. Hence, our code can also be used in cases where the fields dominate the energy density of the universe, for example, during reheating after inflation. We test the algorithm in scenarios of reheating where the inflaton is a complex scalar field with a potential $\propto(2|\varphi|^2-v^2)^2$ and is coupled to an Abelian gauge field. Tracing the evolution of the system through complex dynamics (including resonant excitation of fields, backreaction, formation of solitons, and changes in the equation of state) in a self-consistently expanding universe, we find the energy conservation violation ($<10^{-4}$) to be very stable and the Gauss constraint violation ($<10^{-6}$) to be dominated by differencing noise.