From Cosmic Web to Supernova Remnants: Modeling FRB DM to Trace Baryons across Multiple Scales

Fast radio bursts (FRBs) provide a powerful probe of ionized baryons through their dispersion measures (DMs), but the observed signal contains contributions from the intergalactic medium (IGM), circumgalactic (CGM) gas, host galaxies, and source-local environments. In this thesis, I investigate FRB DMs from cosmic-web to source-local scales using cosmological simulations, zoom-in galaxy simulations, and supernova-remnant (SNR) simulations. Using the CROCODILE simulation suite, I study the DM-$z$ relation, baryon distribution, halo contributions, and host-galaxy DMs. AGN feedback redistributes baryons from halo centers into the diffuse CGM/IGM gas, particularly affecting DM contributions from massive foreground halos. From the simulated DM-$z$ relation, I derive diffuse baryon fractions of $f_{\mathrm{d}\mathrm{i}\mathrm{f}\mathrm{f}}=0.865_{-0.165}^{+0.101}$ and $0.856_{-0.162}^{+0.101}$ for the fiducial and NoBH models. Host-galaxy DM contributions range from below 100 pc cm${}^{-3}$ in dwarf galaxies to above 1300 pc cm${}^{-3}$ in cluster environments. I also model young magnetars embedded in SNRs using one-dimensional hydrodynamical simulations. The dominant time-variable DM component arises from unshocked ejecta, while the shocked region contributes only a minor fraction. Comparisons with FRB 20190520B and FRB 20121102 suggest source-local DM contributions of tens to hundreds of pc cm${}^{-3}$. Most models become transparent to GHz radio emission within 70 yr. In contrast, the shocked region dominates the RM contribution and evolution, with the $11M_{\odot }$ single-star model best reproducing the RM evolution of FRB 20121102. These results demonstrate that FRB dispersion measures must be interpreted as multi-component signals spanning a wide range of physical scales, linking the cosmic web, gaseous halos, host galaxies, and compact-object environments