Closed-Form of the Local Galactic Potential and Stellar Distribution Function from Gaia DR3

Stellar and AGN-driven feedback processes affect the distribution of gas on a wide range of scales, from within galaxies well into the intergalactic medium. Yet, it remains unclear how feedback, through its connection to key galaxy properties, shapes the radial gas density profile in the host halo. We tackle this question using suites of the EAGLE, IllustrisTNG, and Simba cosmological hydrodynamical simulations, which span a variety of feedback models. We develop a random forest algorithm that predicts the radial gas density profile within haloes from the total halo mass and five global properties of the central galaxy: gas and stellar mass; star formation rate; mass and accretion rate of the central black hole (BH). The algorithm reproduces the simulated gas density profiles with an average accuracy of $\sim$83-90% over the halo mass range $10^{9.5} \, \mathrm{M}_{\odot} < M_{\rm 200c} < 10^{15} \, \mathrm{M}_{\odot}$ and redshift interval $0<z<4$. For the first time, we apply Sobol statistical sensitivity analysis to full cosmological hydrodynamical simulations, quantifying how each feature affects the gas density as a function of distance from the halo centre. Across all simulations and redshifts, the total halo mass and the gas mass of the central galaxy are the most strongly tied to the halo gas distribution, while stellar and BH properties are generally less informative. The exact relative importance of the different features depends on the feedback scenario and redshift. Our framework can be readily embedded in semi-analytic models of galaxy formation to incorporate halo gas density profiles consistent with different hydrodynamical simulations. Our work also provides a proof of concept for constraining feedback models with future observations of galaxy properties and of the surrounding gas distribution.

Reconstructing the three-dimensional distribution of dark matter from weak-lensing observations is a central but highly ill-posed inverse problem in cosmology. Unlike standard 3D reconstruction with multiple viewpoints, we observe the universe from a single line of sight, through noisy shape distortions of galaxies with uncertain distances, so meaningful recovery of the 3D matter field requires strong prior assumptions. Existing methods either produce point estimates with handcrafted priors or use neural ensembles for approximate Bayesian uncertainty, and struggle to capture the non-Gaussian, filamentary structure of the cosmic web. With the advent of new high-resolution cosmological simulations, we now have an alternative source of prior knowledge that captures the nonlinear statistics of structure formation with far greater fidelity than analytic prescriptions. We leverage these simulations to build a new dataset $\texttt{Conicus3D}$, which enables us to learn a data-driven diffusion-model prior capturing the full 3D distribution of dark matter structure across cosmic time. Building on recent plug-and-play approaches, we modify a diffusion-based posterior sampling scheme to the 3D weak-lensing setting, combining the learned prior with a differentiable physical forward model. On realistic simulations targeting a modern weak lensing survey, our approach yields substantially improved 2D and 3D reconstruction accuracy over baseline methods. Moreover, it produces posterior samples whose statistics closely track the underlying simulations, while remaining robust to moderate shifts in cosmology.

We perform field-level likelihood-free inference of the matter density parameter $Ω_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $Ω_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $σ_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $Ω_m$ with mean relative errors of about $10\%$ in-distribution and $10$--$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $Ω_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.