Redshift dependence of FRB host dispersion measures across cosmic epochs

We constrain the redshift dependence of (rest frame) host galaxy dispersion measures of localized Fast Radio Bursts (FRBs) by assuming it to vary as a simple power law ($\propto (1+z{)}^{\alpha }$). We simultaneously fit $\alpha$ as well as the host dispersion measure to the data of FRBs with known redshifts. We find that \color{black} $\alpha$ between 0 to 1 is preferred depending upon our modelling choices. Current data can constrain $\mathrm{\mid }\alpha \mathrm{\mid }\lesssim 2$ at a 68 percent confidence interval \color{black}. Such constraints have implications for our understanding of galaxy formation and can be used to inform galaxy and large scale simulations.