  Gravitational wave standard sirens typically require electromagnetic (EM)
data to obtain redshift information to constrain cosmology. Difficult to find
EM counterparts for bright sirens and galaxy survey systematics for dark sirens
make cosmological constraints with spectral sirens, a gravitational wave
data-only approach, extremely appealing. In this work, we use the GWTC-3 BBH
detections as spectral sirens to constrain the BBH population and the
underlying cosmological expansion with a flexible model for the black hole mass
spectrum. We use a binned Gaussian process to model the BBH mass distribution
in the source frame without any astrophysical assumptions on the shape and or
inclusion (or lack of) features that drive the cosmological constraints as the
redshifted detector frame masses become consistent with the underlying
astrophysical mass distribution features. For GWTC-3 we find a measurement on
the Hubble constant of $H_0=73.0^{+13.3}_{-7.7} \ {\rm{km \ s^{-1} \
Mpc^{-1}}}$ at $68\%$ C.L. when combined with that obtained from the bright
standard siren analysis with GW170817 and its associated host galaxy NGC 4993.
We find an improved estimate for the Hubble constant of around a factor of 1.4
times better than the GW170817 measurement alone. We validate our nonparametric
spectral siren approach with simulations and benchmark its scalability and
constraining performance when compared with parametric methods.
