Unravelling the role of cosmic velocity field in dark matter halo mass function using deep learning

Abstract

We discuss an implementation of a deep learning framework to gain insight into the dark matter structure formation. We investigate the impact of velocity and density field information on the construction of halo mass function through cosmological 𝑁-body simulations. In this direction, we train a Convolutional Neural Network (CNN) on the initial snapshot of an only dark matter simulation to predict the halo mass that individual particles fall into at 𝑧 = 0, in the halo mass range of 10.5 < log(𝑀/𝑀 ) < 14. Our results show a negligible improvement from including the velocity in addition to the density information when considering simulations based on the standard model of cosmology (ΛCDM) with the amplitude of initial scalar perturbations 𝐴 𝑠 = 2 × 10 −9 . In order to investigate the ellipsoidal collapse models and to study the effect of velocity in smaller mass ranges, we increase the initial power spectrum such that we see the effect of velocities in larger halos which are in the resolution of our simulation. The CNN model trained on the simulation snapshots with large 𝐴 𝑠 shows a considerable improvement in the halo mass prediction when adding the velocity field information. Eventually, for the simulation with 𝐴 𝑠 = 8 × 10 −8 , the model trained with only density information shows at least 80% increase in the mean squared error relative to the model with both velocity and density information at almost all mass scales, which indicates the failure of the density-only model to predict the halo masses in this case. Our results indicate that the effect of velocity field on the halo collapse is scale-dependent with a negligible effect for the standard model of cosmology in mass scales 10.5 < log(𝑀/𝑀 ) < 14.