Abstract

--- - Context. The large-scale distribution of baryons, commonly referred to as the cosmic web, is sensitive to gravitational collapse, mergers, and galactic feedback processes, and its large-scale structure (LSS) can be classified as halos, filaments, and voids. Fast radio bursts (FRBs) are extragalactic transient radio sources that undergo dispersion along their propagation paths. These systems provide insight into ionised matter along their sightlines by virtue of their dispersion measures (DMs), and have been investigated as probes of the LSS baryon fraction, the diffuse baryon distribution, and of cosmological parameters. Such efforts are highly complementary to the study of intergalactic medium (IGM) through X-ray observations, the Sunyaev-Zeldovich effect, and galaxy populations. - Aims. We use the cosmological simulation IllustrisTNG to study FRB DMs accumulated while traversing different types of LSS. - Methods. We combined methods for deriving electron density, classifying LSS, and tracing FRB sightlines through TNG300-1. We identified halos, filaments, voids, and collapsed structures along randomly selected sightlines, and calculated their DM contributions. - Results. We present a comprehensive analysis of the redshift-evolving cosmological DM components of the cosmic web. We find that the filamentary contribution to DM dominates, increasing from similar to 71% to similar to 80% on average for FRBs originating at z = 0.1 versus z = 5, while the halo contribution falls, and the void contribution remains consistent to within similar to 1%. The majority of DM variance between sightlines originates from halo and filamentary environments, potentially making void-only sightlines more precise probes of cosmological parameters. We find that, on average, an FRB originating at z = 1 will intersect similar to 1.8 foreground collapsed structures of any mass, with this value increasing to similar to 12.4 structures for an FRB originating at z = 5. The measured impact parameters between our sightlines and TNG structures of any mass appear consistent with those reported for likely galaxy-intersecting FRBs. However, we measure lower average accumulated DMs from these structures than the similar to 90 pc cm(-3) DM excesses reported for these literature FRBs, indicating that some of this DM may arise from beyond the structures themselves.