Striking a Chord with Spectral Sirens: multiple features in the compact binary population correlate with $H_0$

Spectral siren measurements of the Hubble constant ($H_0$) rely on correlations between observed detector-frame masses and luminosity distances. Features in the source-frame mass distribution can induce these correlations. It is crucial, then, to understand (i) which features in the source-frame mass distribution are robust against model (re)parametrization, (ii) which features carry the most information about $H_0$, and (iii) whether distinct features independently correlate with cosmological parameters. We study these questions using real gravitational-wave observations from the LIGO-Virgo-KAGRA Collaborations' third observing run. Although constraints on $H_0$ are weak, we find that current data reveals several prominent features in the mass distribution, including peaks in the binary black hole source-frame mass distribution near $\sim$ 9 $\rm{M}_{\odot}$ and $\sim$ 32$\rm{M}_{\odot}$ and a roll-off at masses above $\sim$ 46$\rm{M}_{\odot}$. For the first time using real data, we show that all of these features carry cosmological information and that the peak near $\sim$ 32$\rm{M}_{\odot}$ consistently correlates with $H_0$ most strongly. Introducing model-independent summary statistics, we show that these statistics independently correlate with $H_0$, exactly what is required to limit systematics within future spectral siren measurements from the (expected) astrophysical evolution of the mass distribution.