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In modified gravity models that allow for additional non-compact spacetimedimensions, energy from gravitational waves can leak into these extra spacetimedimensions, leading to a reduction in the amplitude of the observedgravitational waves, and thus a source of potential systematics in the inferredluminosity 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 thusbe able to break the mass-redshift degeneracy. We simultaneously fit for theBBH population and the extra spacetime dimensions parameters from gravitationalleakage models using BBH observations from the recently released GWTC-3catalog. 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 ascreening scale, finding that the GWTC-3 constraint is as competitive as thatset from GW170817 and its electromagnetic counterpart. For models where gravityleaks 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 areconstrained jointly with the BBH population at cosmological distances. Theseconstraints are consistent with General Relativity (GR) where gravitationalwaves propagate in $D=3+1$ spacetime dimensions. Using the BBH population toprobe modifications to standard cosmological models provides an independenttest of GR that does not rely on any electromagnetic information but purely ongravitational wave observations.

Constraining the number of spacetime dimensions from GWTC-3 binary black hole mergers