Growth of a Black Hole in a Scalar Field Cosmology

We present results from numerical relativity simulations investigating the accretion behavior of a non-spinning black hole embedded in a cosmological background driven by a scalar field. The simulations employ a modified moving-puncture gauge condition adapted for cosmological spacetimes. Considering inflationary potentials, we derive a black hole mass-growth relation within the dynamical horizon framework and validate it through our numerical results. We find that the accretion rate scales as $\dot{M} \propto M^2$, where $M$ is the black hole mass, and that $\dot{M} \propto \dot{\varphi}^2$. The simulations confirm consistency with the derived mass-growth formula. Interestingly, the scalar field dynamics near the black hole show little deviation from those in the far-field cosmological region. In some cases, the black hole grows by as much as 15% of its initial mass before the scalar field settles at the minimum of its potential.