Gauge preheating with full general relativity

We study gauge preheating following pseudoscalar-driven inflation in full general relativity. We implement the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) scheme to solve the full nonlinear evolution of the metric alongside the dynamics of the pseudoscalar and gauge fields. The dynamics of the background and emission of gravitational waves are broadly consistent with simulations in a Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) spacetime. We find large, localized overdensities in the BSSN simulations of order $\delta = \delta\rho/\rho \sim 30$, and the dimensionless power spectrum of $\delta$ peaks above unity. These overdense regions are seeded on length scales only slightly smaller than the horizon, and have a compactness $C \sim 0.1$. The scale of peak compactness is shorter than the Jeans length, which implies that pressure of the matter fields plays an important role in the evolution of these objects.