Islands in Simulated Cosmos: Probing the Hubble Flow around Groups and Clusters

The local Hubble flow provides a valuable probe of the transition between cosmic expansion and nonlinear gravitational dynamics. On large scales, galaxies follow the linear Hubble law, but within group- and cluster-sized environments, gravitational interactions generate substantial deviations. Using the IllustrisTNG cosmological simulations, we test whether dark energy leaves measurable signatures in the local velocity radius relation. We model the kinematics with extensions of the Lema\^{\i}tre Tolman framework and use Bayesian inference to recover halo masses and the Hubble constant $H_0$. The fits exhibit systematic biases: halo masses are recovered with a median ratio $\big\langle M_{\rm fit}/M_{\rm true}\big\rangle = 0.991 \pm 0.148$, while the inferred expansion rate peaks at $\big\langle H_{0,\text{fit}}/H_{0,\text{True}} \big\rangle =1.01 \pm 0.14$. Although both mass and $H_0$ can be constrained from the local flow, the different model variants, as the angular momentum, friction-like terms, or dark energy, remain statistically indistinguishable given the intrinsic environmental variance. Our results demonstrate both the potential and the fundamental limitations of using local kinematics as a precision diagnostic of dark energy.