Learning the Universe with cosmological rescaling of merger trees and semi-analytic galaxy formation models

Abstract

Learning cosmology from galaxy surveys requires large suites of simulations spanning the cosmological and astrophysical parameter space, yet hydrodynamical simulations of galaxy formation remain prohibitively expensive. Semi-analytic models offer an inexpensive, physically grounded alternative, but still require halo merger trees from $N$-body simulations, and densely sampling cosmological parameters in sufficient volume remains expensive. We address this by extending cosmological rescaling to operate directly on merger trees and applying it in the $\Omega_{\rm m}$-$\sigma_8$ plane, running the Santa Cruz semi-analytic model for galaxy formation on the rescaled trees to produce galaxy populations across new cosmological and astrophysical parameters at negligible additional cost. A novel halo-profile-based correction, controlled by a single free parameter, suppresses systematic bias in rescaled halo masses to below the per cent level. We apply the method to parameter estimation of $\Omega_{\rm m}$ and $\sigma_8$ given either the stellar mass function or the two-point correlation function, finding that as few as 64, and potentially fewer, base $N$-body simulations, rescaled to $\sim1000$ training samples, match the accuracy of 750 dedicated $N$-body simulations; rescaling to 3200 realisations improves the prediction of $\Omega_{\rm m}$ by $\sim25\%$. Rescaling all merger trees from a single CAMELS-SAM $N$-body simulation costs $\sim0.1$ CPUh, compared to several thousand CPUh to run the simulation itself. We demonstrate a practical route to obtaining predictions of galaxy summary statistics across cosmological and astrophysical parameters, even with a relatively small number of base $N$-body simulations.