MG-NECOLA: A Field-Level Emulator for $f(R)$ Gravity and Massive Neutrino Cosmologies

TL;DR

MG-NECOLA is a neural network-based emulator that enhances approximate MG-PICOLA simulations to near-$N$-body accuracy, enabling fast, precise modeling of non-linear cosmological structures for modified gravity and neutrino studies.

Contribution

It introduces a convolutional neural network emulator trained on MG simulations that generalizes well across cosmologies, significantly reducing computational costs while maintaining high accuracy.

Findings

Achieves sub-percent accuracy in matter power spectrum and bispectrum up to $k \,\simeq\ 1\,h\mathrm{Mpc}^{-1}$.

Generalizes robustly to cosmologies outside training set with errors below 5%.

Provides a speed-up factor of approximately 1500 times compared to full $N$-body simulations.

Abstract

Accurate modeling of non-linear gravitational dynamics is essential for constraining extensions to the standard cosmological model using large-scale structure observations. While high-resolution $N$-body simulations provide the required fidelity, they are computationally prohibitive for the large ensembles needed to analyze Modified Gravity (MG) scenarios. We present MG-NECOLA, a field-level emulator based on a convolutional neural network that upgrades fast, approximate MG-PICOLA simulations to near--$N$-body accuracy at a fraction of the computational cost. Trained on a suite of QUIJOTE_MG simulations for $f(R)$ gravity, MG-NECOLA achieves nearly sub-percent accuracy ($\lesssim 1\%$) in both the matter power spectrum and bispectrum up to $k \simeq 1~h\,\mathrm{Mpc}^{-1}$. Crucially, although being trained on a fixed cosmology, the network generalizes robustly to cosmologies outside its training manifold keeping the error below $5\%$. It successfully recovers the General Relativity limit ($\Lambda$CDM) without introducing spurious MG signals and accurately captures the power suppression induced by massive neutrinos ($M_\nu \leq 0.4$ eV), despite being trained on cosmologies with massless neutrinos. The pipeline delivers a speed-up factor of $\sim 1500\times$ relative to full $N$-body runs, generating a high-fidelity realization in O$(10^3)$ CPU seconds compared to O$(10^6)$ for the baseline. This accuracy-efficiency trade-off establishes MG-NECOLA as a powerful tool for generating the massive mock catalogs required for next-generation galaxy surveys.