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Abstract We discover analytic equations that can infer the value of Ω_mfrom the positions and velocity moduli of halo and galaxy catalogs. The equations are derived by combining a tailored graph neural network (GNN) architecture with symbolic regression. We first train the GNN on dark matter halos from GadgetN-body simulations to perform field-level likelihood-free inference, and show that our model can infer Ω_mwith ∼6% accuracy from halo catalogs of thousands ofN-body simulations run with six different codes: Abacus, CUBEP³M, Gadget, Enzo, PKDGrav3, and Ramses. By applying symbolic regression to the different parts comprising the GNN, we derive equations that can predict Ω_mfrom halo catalogs of simulations run with all of the above codes with accuracies similar to those of the GNN. We show that, by tuning a single free parameter, our equations can also infer the value of Ω_mfrom galaxy catalogs of thousands of state-of-the-art hydrodynamic simulations of the CAMELS project, each with a different astrophysics model, run with five distinct codes that employ different subgrid physics: IllustrisTNG, SIMBA, Astrid, Magneticum, SWIFT-EAGLE. Furthermore, the equations also perform well when tested on galaxy catalogs from simulations covering a vast region in parameter space that samples variations in 5 cosmological and 23 astrophysical parameters. We speculate that the equations may reflect the existence of a fundamental physics relation between the phase-space distribution of generic tracers and Ω_m, one that is not affected by galaxy formation physics down to scales as small as 10h⁻¹kpc. 

Abstract We measure the clustering of Lyman Alpha Emitting galaxies (LAEs) selected from the One-hundred-square-degree DECam Imaging in Narrowbands (ODIN) survey, with spectroscopic follow-up from Dark Energy Spectroscopic Instrument (DESI). We use DESI spectroscopy to optimize our selection and to constrain the interloper fraction and redshift distribution of our narrow-band selected sources. We select samples of 4000 LAEs atz= 2.45 and 3.1 in 9 sq.deg. centered on the COSMOS field with median Lyα fluxes of ≈ 10^-16erg s^-1cm^-2. Covariances and cosmological inferences are obtained from a series of mock catalogs built upon high-resolution N-body simulations that match the footprint, number density, redshift distribution and observed clustering of the sample. We find that both samples have a correlation length ofr₀= 3.0 ± 0.2 h^-1Mpc. Within our fiducial cosmology these correspond to 3D number densities of ≈ 10^-3h³Mpc^-3and, from our mock catalogs, biases of 1.7 and 2.0 atz= 2.45 and 3.1, respectively. We discuss the implications of these measurements for the use of LAEs as large-scale structure tracers for high-redshift cosmology. 

Abstract We train graph neural networks on halo catalogs from Gadget N -body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogs contain ≲5000 halos with masses ≳10 10 h −1 M ⊙ in a periodic volume of ( 25 h − 1 Mpc ) 3 ; every halo in the catalog is characterized by several properties such as position, mass, velocity, concentration, and maximum circular velocity. Our models, built to be permutationally, translationally, and rotationally invariant, do not impose a minimum scale on which to extract information and are able to infer the values of Ω m and σ 8 with a mean relative error of ∼6%, when using positions plus velocities and positions plus masses, respectively. More importantly, we find that our models are very robust: they can infer the value of Ω m and σ 8 when tested using halo catalogs from thousands of N -body simulations run with five different N -body codes: Abacus, CUBEP 3 M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer Ω m also works when tested on thousands of state-of-the-art CAMELS hydrodynamic simulations run with four different codes and subgrid physics implementations. Using halo properties such as concentration and maximum circular velocity allow our models to extract more information, at the expense of breaking the robustness of the models. This may happen because the different N -body codes are not converged on the relevant scales corresponding to these parameters.