Cosmology with one galaxy: An analytic formula relating $Ω_{\rm m}$ with galaxy properties

TL;DR

This work demonstrates that the matter density parameter $Ω_m$ leaves a measurable imprint on individual galaxies, enabling an analytic cosmology tracer derived from galaxy observables. Using symbolic regression on CAMELS simulations, the authors uncover a compact, interpretable functional form that robustly recovers $Ω_m$ across multiple simulation suites and redshifts, with a shared latent structure tied to baryon retention and metallicity regulation. The physically grounded predictor, built from dimensionless galaxy properties, connects local baryonic processing to global cosmology through a sigmoidal, log-transformed mapping and a mild morphology term, and extends to extended parameter spaces (TNG-SB28) where a retention-efficiency term emerges. These results offer a complementary pathway to precision cosmology, bridging small-scale galaxy physics and large-scale cosmic parameters, and motivating observational tests within a gas-regulator framework.

Abstract

Standard cosmological analyses typically treat galaxy formation and cosmological parameter inference as decoupled problems, relying on population-level statistics such as clustering, lensing, or halo abundances. However, classical studies of baryon fractions in massive galaxy clusters have long suggested that gravitationally bound systems may retain cosmological information through their baryonic content. Building on this insight, we present the first analytic and physically interpretable cosmological tracer that links the matter density parameter, $Ω_m$, directly to intrinsic galaxy-scale observables, demonstrating that cosmological information can be extracted from individual galaxies. Using symbolic regression applied to state-of-the-art hydrodynamical simulations from the CAMELS project, we identify a compact functional form that robustly recovers $Ω_m$ across multiple simulation suites (IllustrisTNG, ASTRID, SIMBA, and Swift-EAGLE), requiring only modest recalibration of a small number of coefficients. The resulting expression admits a transparent physical interpretation in terms of baryonic retention and enrichment efficiency regulated by gravitational potential depth, providing a clear explanation for why $Ω_m$ is locally encoded in galaxy properties. Our work establishes a direct, interpretable bridge between small-scale galaxy physics and large-scale cosmology, opening a complementary pathway to cosmological inference that bypasses traditional clustering-based statistics and enables new synergies between galaxy formation theory and precision cosmology.

Figures (8)

• Figure 1: Symbolic regression search loop: The procedure starts with initialization (Init.), evaluates candidate expressions (Eval.), and applies selection and modification operators to generate new equations. A stopping condition is then checked; if satisfied, the algorithm terminates and outputs the resulting expression, otherwise the search continues iteratively.
• Figure 2: Performance of the analytic $\Omega_m$ predictor across four simulation suites at $z=0$. Each panel compares predicted versus true $\Omega_m$ for galaxies from the IllustrisTNG, ASTRID, SIMBA, and Swift-EAGLE simulations. Points are binned using a hexagonal grid and colored by the base-10 logarithm of the number of galaxies in each bin. The dashed line denotes perfect prediction, and the quoted $R^2$, and accuracy values summarize performance in linear space.
• Figure 3: Performance of the analytic $\Omega_m$ predictor across different redshifts. Each panel compares predicted and true $\Omega_m$ values. Top row: IllustrisTNG. Bottom row: ASTRID. Colors represent the logarithmic number density per hexagonal bin. The dashed red line indicates perfect prediction.
• Figure 4: Stellar mass--metallicity relations (MZR) at redshift $z=0$ for the IllustrisTNG (left) and Astrid (right) simulation suites. Each point represents an individual galaxy colored by its feedback parameters $A_{\mathrm{SN1}}, A_{\mathrm{SN2}}, A_{\mathrm{AGN1}},$ and $A_{\mathrm{AGN2}}$. The dashed black lines show the best--fit power--law trends in $\log M_\star$--$Z_\star$ space, with annotated $R^2$ values quantifying the correlation strength. These relations illustrate that both simulations exhibit similar MZR slopes and feedback‐driven metallicity modulation, providing a baseline comparison for the analytic $\Omega_m$ tracer model.
• Figure 5: Performance of the analytic $\Omega_m$ predictor on the TNG-SB28 dataset for different redshifts. Each panel contains a combined diagnostic: a hexbin density plot (left) comparing true versus predicted $\Omega_m$ and a calibration curve (right) showing the median prediction in bins of the true value with 16--84th percentile bands. Results are shown for redshifts $z = 0.0, 1.0, 2.0, 3.0$ (top-left to bottom-right). A saturation regime appears at high $\Omega_m$ (indicated by doted horizontal red lines, of $\Omega_m$$\simeq$ 0.43) in all cases, indicating a limit beyond which galaxy properties no longer carry independent cosmological information under the SB28 parameter variations.