  In modified gravity models that allow for additional non-compact spacetime
dimensions, energy from gravitational waves can leak into these extra spacetime
dimensions, leading to a reduction in the amplitude of the observed
gravitational waves, and thus a source of potential systematics in the inferred
luminosity distances to gravitational wave sources. Since binary black hole
(BBH) mergers are standard sirens, we use the pair-instability supernova
(PISNe) mass gap and its predicted features to determine a mass scale and thus
be able to break the mass-redshift degeneracy. We simultaneously fit for the
BBH population and the extra spacetime dimensions parameters from gravitational
leakage models using BBH observations from the recently released GWTC-3
catalog. We set constraints on the number of spacetime dimensions and find that
$D= 3.95^{+0.09}_{-0.07}$ at $68\%$ C.L. for models that are independent of a
screening scale, finding that the GWTC-3 constraint is as competitive as that
set from GW170817 and its electromagnetic counterpart. For models where gravity
leaks below a certain screening scale $R_c$, we find $D=4.23^{+1.50}_{-0.57}$
and $\log_{10} R_c/{\rm Mpc}= 4.14^{+0.55}_{-0.86}$ with a transition steepness
$\log_{10} n = 0.86^{+0.73}_{-0.84}$ for the leakage, which for the first are
constrained jointly with the BBH population at cosmological distances. These
constraints are consistent with General Relativity (GR) where gravitational
waves propagate in $D=3+1$ spacetime dimensions. Using the BBH population to
probe modifications to standard cosmological models provides an independent
test of GR that does not rely on any electromagnetic information but purely on
gravitational wave observations.
