The DREAMS Project: A New Suite of 1,024 Simulations to Contextualize the Milky Way and Assess Physics Uncertainties

We introduce a new suite of 1,024 cosmological and hydrodynamical zoom-in simulations of Milky Way-mass halos, run with Cold Dark Matter, as part of the DREAMS Project. Each simulation in the suite has a unique set of initial conditions and combination of cosmological and astrophysical parameters. The suite is designed to quantify theoretical uncertainties from halo-to-halo variance, as well as stellar and black hole feedback. We develop a novel weighting scheme that prioritizes regions of the input parameter space, yielding galaxies consistent with the observed present-day stellar mass--halo mass relation. The resulting galaxy population exhibits a wide diversity in structural properties that encompasses those of the actual Milky Way, providing a powerful statistical sample for galactic archaeology. To demonstrate the suite's scientific utility, we investigate the connection between a galaxy's merger history, focusing on Gaia-Sausage-Enceladus~(GSE) analogs, and its present-day properties. We find that galaxies with a GSE analog have lower star formation rates, more compact disks, and more spherical stellar halos. Crucially, significant halo-to-halo scatter remains, demonstrating that matching more than the most significant events in the Milky Way's past is necessary to recover its present-day properties. Our results highlight the necessity for large statistical samples to disentangle the stochastic nature of galaxy formation and robustly model the Milky Way's unique history.