Emulation of f(R) modified gravity from ΛCDM using conditional GANs

A major aim of cosmological surveys is to test deviations from the standard ΛCDM 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 ΛCDM 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 ΛCDM 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 ~ 2\, hMpc⁻¹$. But for a few select cases, higher order statistics are reproduced with $$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 $Λ$CDM simulation, the GPU-based emulator can reproduce the equivalent $f(R)$ realization $~$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.