Emulation of <i>f(R)</i> modified gravity from ΛCDM using conditional GANs

ABSTRACT 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 realized 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 generalize our emulator to $f(R)$ models with differing field strengths. The predictions of our emulator agree with the $f(R)$ simulations to within 5 per cent for matter density and to within 10 per cent 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 per cent agreement. Latent extrapolation allows our emulator to generalize to different parametrizations of the $f(R)$ model without explicitly training on those variants. Given a $\Lambda$CDM simulation, the GPU-based emulator can reproduce the equivalent $f(R)$ realization $\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.