A universal equation to predict $\Omega_{\rm m}$ from halo and galaxy catalogues
Abstract
We discover analytic equations that can infer the value of $\Omega_{\rm m}$ from the positions and velocity moduli of halo and galaxy catalogues. 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 Gadget Nbody simulations to perform fieldlevel likelihoodfree inference, and show that our model can infer $\Omega_{\rm m}$ with $\sim6\%$ accuracy from halo catalogues of thousands of Nbody simulations run with six different codes: Abacus, CUBEP$^3$M, Gadget, Enzo, PKDGrav3, and Ramses. By applying symbolic regression to the different parts comprising the GNN, we derive equations that can predict $\Omega_{\rm m}$ from halo catalogues 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 $\Omega_{\rm m}$ from galaxy catalogues of thousands of stateoftheart 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, SWIFTEAGLE. Furthermore, the equations also perform well when tested on galaxy catalogues 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 phasespace distribution of generic tracers and $\Omega_{\rm m}$, one that is not affected by galaxy formation physics down to scales as small as $10~h^{1}{\rm kpc}$.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.14591
 arXiv:
 arXiv:2302.14591
 Bibcode:
 2023arXiv230214591S
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 32 pages, 13 figures, summary video: https://youtu.be/STZHvDHkVgo