Emulating Halo Statistics for Large-Scale Structure Cosmology

Dark matter halos are fundamental building blocks for the hierarchical structure formation in the Universe seen over different mass scales. An accurate model of their statistical properties is essential for a proper interpretation of observational data. Cosmological N-body simulations have been serving as a powerful tool for this purpose. However, the high computational cost prevents us from using them to fully explore the halo statistics in a multi-dimensional cosmological parameter space, especially for parameter inference. We have been conducting a simulation campaign named "Dark Quest" to overcome this difficulty. The first result of this campaign consists of $2048^3$-body simulations at 100 cosmological parameter sets both in high (box size of $1h^{-1}$Gpc) and low ($2h^{-1}$Gpc) resolution modes. The key ideas are i) an efficient sampling scheme to cover a multi-dimensional space, ii) nonparametric regression based on Gaussian Process, and iii) careful cross validation studies to ensure the accuracy of the statistical model. Our python package "Dark Emulator" predicts basic halo statistics (the mass function and auto and cross correlation functions) for halos more massive than $10^{12}h^{-1}M_\odot$ in a six-parameter flat wCDM cosmology within $\sim 100$ milliseconds on a standard laptop computer. This is contrasted to $\sim 2$ days needed to perform a new simulation on about 600 CPU cores on a supercomputer. Further, an HOD model can map the emulator outputs to galaxy statistics.