Beyond ΛCDM: Deep Generative Models for Modified Gravity

Abstract

Accurate modelling of the late-time matter distribution is essential for testing cosmological scenarios beyond ΛCDM, especially in the non-linear regime where modified-gravity signatures are most prominent. However, obtaining field-level predictions in such scenarios remains challenging: high-fidelity N-body simulations are computationally expensive, while fast approximate methods sacrifice accuracy on the scales where departures from General Relativity are most relevant. In this thesis, our goal is to bridge this gap by training diffusion models directly on matter density fields and testing whether they can reproduce both the morphology and the clustering statistics of modified-gravity simulations. In this thesis, we develop and assess denoising diffusion probabilistic models (DDPMs) as field-level generative emulators for the f(R) model of modified gravity. We adopt a two-tier simulation strategy based on MG-PICOLA and MG-QUIJOTE. We construct two-dimensional density slices from the three-dimensional matter field, compare two slicing strategies, study the effect of slice thickness, and train both unconditional and conditional DDPMs. The unconditional model is trained on a fixed f(R) cosmology, while the conditional model is trained across four f(R) gravity strengths, fR₀ = −5×10⁻⁷, −5×10⁻⁶, −5×10⁻⁵, and −5×10⁻⁴, corresponding to the classes fR_p, fR_pp, fR_ppp, and fR_pppp. We show that Method 1 with slice thickness = 1 provides the best-performing data representation for two-dimensional generative modelling. For the unconditional case, we show that the DDPM reproduces the visual morphology of the cosmic web and recovers the target two-point statistics with high fidelity. In the best-performing configuration, the transfer function remains within approximately 5% of unity over the range 0.01 ≲ k ≲ 0.4 h Mpc⁻¹, with the main residual discrepancies confined to the highest-k regime. For the conditional case, we show that the model learns the expected ordering across modified-gravity classes and preserves the relative dependence of clustering on |fR0|. Quantitatively, the generated spectra remain within approximately ±10% of the target spectra over 0.01 ≲ k ≲ 0.5 h Mpc⁻¹, while the overall performance shows a mild degradation as the strength of the modified-gravity parameter increases. Overall, we demonstrate that diffusion models provide a promising framework for fast and flexible field-level emulation of modified-gravity density fields