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The Macquart relation describes the correlation between the dispersionmeasure (DM) of fast radio bursts (FRBs) and the redshift $z$ of their hostgalaxies. The scatter of the Macquart relation is sensitive to the distributionof baryons in the intergalactic medium (IGM) including those ejected fromgalactic halos through feedback processes. The width of the distribution in DMsfrom the cosmic web (${\rm DM}_{\rm cosmic}$) is parameterized by a fluctuationparameter $F$, which is related to the cosmic DM variance by $\sigma_{\rm DM}=F z^{-0.5}$. In this work, we present a new measurement of $F$ using 78 FRBs ofwhich 21 have been localized to host galaxies. Our analysis simultaneously fitsfor the Hubble constant $H_0$ and the DM distribution due to the FRB hostgalaxy. We find that the fluctuation parameter is degenerate with theseparameters, most notably $H_0$, and use a uniform prior on $H_0$ to measure$\log_{10} F > -0.89$ at the $3\sigma$ confidence interval and a new constrainton the Hubble constant $H_0 = 85.3_{-8.1}^{+9.4} \, {\rm km \, s^{-1} \,Mpc^{-1}}$. Using a synthetic sample of 100 localized FRBs, the constraint onthe fluctuation parameter is improved by a factor of $\sim 2$. Comparing our$F$ measurement to simulated predictions from cosmological simulation(IllustrisTNG), we find agreement between $0.4 < z < 2$. However, at $z < 0.4$,the simulations underpredict $F$ which we attribute to the rapidly changingextragalactic DM excess distribution at low redshift.

Measuring the Variance of the Macquart Relation in z-DM Modeling