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

Abstract: 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 $\Lambda$CDM to include dynamical dark energy (characterized by $w_0$ and $w_a$), massive neutrinos ($\sum m_\nu$), the effective number of neutrinos ($N_\text{eff}$), and running of the spectral index ($\alpha_\text{s}$). 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.