Ten-dimensional neural network emulator for the nonlinear matter power spectrum

We present GokuNEmu, a ten-dimensional neural network emulator for the nonlinear matter power spectrum, designed to support next-generation cosmological analyses. Built on the Goku $N$-body simulation suite and the T2N-MusE emulation framework, GokuNEmu predicts the matter power spectrum with $\sim 0.5 %$ average accuracy for redshifts $0 \leq z \leq 3$ and scales $0.006 \leq k/(h,\mathrm{Mpc}^{-1}) \leq 10$. The emulator models a 10D parameter space that extends beyond $Λ$CDM to include dynamical dark energy (characterized by $w_0$ and $w_a$), massive neutrinos ($\sum m_ν$), the effective number of neutrinos ($N_\text{eff}$), and running of the spectral index ($α_\text{s}$). Its broad parameter coverage, particularly for the extensions, makes it the only matter power spectrum emulator capable of testing recent dynamical dark energy constraints from DESI. In addition, it requires only $\sim $2 milliseconds to predict a single cosmology on a laptop, orders of magnitude faster than existing emulators. These features make GokuNEmu a uniquely powerful tool for interpreting observational data from upcoming surveys such as LSST, Euclid, the Roman Space Telescope, and CSST.

💡 Research Summary

The paper introduces GokuNEmu, a ten‑dimensional neural‑network emulator designed to predict the nonlinear matter power spectrum with sub‑percent accuracy across a wide range of cosmological models. Built on the Goku N‑body simulation suite and the T2N‑MusE emulation framework, GokuNEmu covers redshifts 0 ≤ z ≤ 3 and wavenumbers 0.006 ≤ k ≤ 10 h Mpc⁻¹, achieving an average relative error of about 0.5 % while delivering predictions in roughly 2 ms on a standard laptop.

The emulator’s parameter space includes the five base ΛCDM parameters (Ω_m, Ω_b, h, A_s, n_s) plus four extensions that are increasingly relevant for modern cosmology: dynamical dark energy (w₀, wₐ), the sum of neutrino masses (∑m_ν), the effective number of relativistic species (N_eff), and the running of the primordial spectral index (α_s). The prior ranges are deliberately broad—e.g., w₀ ∈