Growth of a Black Hole in a Scalar Field Cosmology

We present a numerical relativity study of the accretion properties of a non-spinning black hole in a cosmology driven by a scalar field. The simulations are carried out with a modified moving-puncture gauge condition suitable for cosmological space-times. We considered a scalar field with potential $V=\lambda \,\varphi^4/4$ and derived the black hole mass growth formula for this scenario using the dynamical horizon framework. As with perturbative studies, we find that the accretion rate $\dot M \propto M^2$ with $M$ the mass of the black hole, and that $\dot M \propto \dot\varphi^2$. We verify that the results of the simulations satisfy the mass growth formula. Unexpectedly, the dynamics of the scalar field in the neighborhood of the black hole is not significantly different from the behavior of the field far away from the hole. We found situations in which the black hole can growth $\sim 15\%$ of its initial mass before the scalar field reaches the bottom of its potential.