Cosmology with One Galaxy: Auto-Encoding the Galaxy Properties Manifold
Cosmological simulations like CAMELS and IllustrisTNG characterize hundreds of thousands of galaxies using various internal properties. Previous studies have demonstrated that machine learning can be used to infer the cosmological parameter $Ω_m$ from the internal properties of even a single randomly selected simulated galaxy. This ability was hypothesized to originate from galaxies occupying a low-dimensional manifold within a higher-dimensional galaxy property space, which shifts with variations in $Ω_m$. In this work, we investigate how galaxies occupy the high-dimensional galaxy property space, particularly the effect of $Ω_m$ and other cosmological and astrophysical parameters on the putative manifold. We achieve this by using an autoencoder with an Information-Ordered Bottleneck (IOB), a neural layer with adaptive compression, to perform dimensionality reduction on individual galaxy properties from CAMELS simulations, which are run with various combinations of cosmological and astrophysical parameters. We find that for an autoencoder trained on the fiducial set of parameters, the reconstruction error increases significantly when the test set deviates from fiducial values of $Ω_m$ and $A_{\text{SN1}}$, indicating that these parameters shift galaxies off the fiducial manifold. In contrast, variations in other parameters such as $σ_8$ cause negligible error changes, suggesting galaxies shift along the manifold. These findings provide direct evidence that the ability to infer $Ω_m$ from individual galaxies is tied to the way $Ω_m$ shifts the manifold. Physically, this implies that parameters like $σ_8$ produce galaxy property changes resembling natural scatter, while parameters like $Ω_m$ and $A_{\text{SN1}}$ create unsampled properties, extending beyond the natural scatter in the fiducial model.