Extended Data Fig. 3: Examples of cosmic DM distributions for different redshifts and cosmic baryon parameters.

The two upper rows show the 2D P(DM_IGM, DM_X) distribution, which is the relative probability in DM_IGM and DM_X for FRBs at z_s = 0.5 (top) and z_s = 1.0 (middle) for increasing values of the halo gas fraction, f_X. We use a bivariate log-normal distribution that has been calibrated to mock FRB surveys in the Illustris TNG300-1 simulation. The distribution ensures that DM_IGM and DM_X are correlated, since sightlines that pass through halos are more likely to pass through overdensities in the cosmic web and have large DM_IGM. In order to compute our final likelihood function, the 2D distribution shown in the top two rows must be integrated along curves of constant cosmic DM, \({{\rm{DM}}}_{\cos }={{\rm{DM}}}_{{\rm{IGM}}}+{{\rm{DM}}}_{{\rm{X}}}\). The resulting \(P({{\rm{DM}}}_{{\rm{ex}}}| {z}_{\rm s},\overrightarrow{\theta })\) are show in the bottom row, with μ_host = 4.5 and σ_host = 0.7. The bottom left and bottom right likelihoods are not supported by our data.