Emulation of $f(R)$ modified gravity from $\Lambda$CDM using conditional GANs

A major aim of cosmological surveys is to test deviations from the standard $\Lambda$CDM model, but the full scientific value of these surveys will only be realised through efficient simulation methods that keep up with the increasing volume and precision of observational data. $N$-body simulations of modified gravity (MG) theories are computationally expensive since highly non-linear equations must be solved. This represents a significant bottleneck in the path to reach the data volume and resolution attained by equivalent $\Lambda$CDM simulations. We develop a field-level neural network-based emulator that generates density and velocity divergence fields under the $f(R)$ gravity MG model from the corresponding $\Lambda$CDM simulated fields. Using attention mechanisms and a complementary frequency-based loss function, our model is able to learn this intricate mapping. We use the idea of latent space extrapolation to generalise our emulator to $f(R)$ models with differing field strengths. The predictions of our emulator agree with the $f(R)$ simulations to within 5% for matter density and to within 10% for velocity divergence power spectra up to $k \sim 2\,h$ $\mathrm{Mpc}^{-1}$. But for a few select cases, higher-order statistics are reproduced with $\lesssim$10% agreement. Latent extrapolation allows our emulator to generalise to different parameterisations of the $f(R)$ model without explicitly training on those variants. Given a $\Lambda$CDM simulation, the GPU-based emulator can reproduce the equivalent $f(R)$ realisation $\sim$600 times faster than full $N$-body simulations. This lays the foundations for a valuable tool for realistic yet rapid mock field generation and robust cosmological analyses.