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

Abstract: 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.