Cosmic variance poses limits to the analyses of the physics of the nearby Universe. For example, it hinders establishing an accurate observational link between halo formation history and galaxy properties or constraining the physics of Dark Matter. The BORG framework offers a way out by generating constrained initial conditions which reproduce all the Large scale structures in a simulated environment with minimal effects due to cosmic variance. By relying on the physics of gravitational interaction and our knowledge of the Universe on large scales, it can generate an ensemble of plausible samples of the initial conditions of our Universe. That framework unlocks the possibility of studying different models of galaxy formation and their impact on different observed environments. The physical environment is notably responsible for the specific mass accretion history of small-scale structures. The Sibelius-Dark simulation is an effort in that direction. I will showcase some direct results obtained with this simulation, and also more generally by the BORG framework on e.g. gravitational lensing and upper bound on the cross-section of Dark Matter particles.
