At present, we have almost as many theories to explain Fast Radio Bursts as we have Fast Radio Bursts observed. This landscape will be changing rapidly with CHIME/FRB, recently commissioned in Canada, and HIRAX, under construction in South Africa. This is an opportune time to review existing theories and their observational consequences, allowing us to efficiently curtail viable astrophysical models as more data becomes available. In this article we provide a currently up to date catalogue of the numerous and varied theories proposed for Fast Radio Bursts so far. We also launched an online evolving repository for the use and benefit of the community to dynamically update our theoretical knowledge and discuss constraints and uses of Fast Radio Bursts.

We consider the possible observation of Fast Radio Bursts (FRBs) with planned future radio telescopes, and investigate how well the dispersions and redshifts of these signals might constrain cosmological parameters. We construct mock catalogues of FRB dispersion measure (DM) data and employ Markov Chain Monte Carlo (MCMC) analysis, with which we forecast and compare with existing constraints in the flat ΛCDM model, as well as some popular extensions that include dark energy equation of state and curvature parameters. We find that the scatter in DM observations caused by inhomogeneities in the intergalactic medium (IGM) poses a big challenge to the utility of FRBs as a cosmic probe. Only in the most optimistic case, with a high number of events and low IGM variance, do FRBs aid in improving current constraints. In particular, when FRBs are combined with CMB+BAO+SNe+H 0 data, we find the biggest improvement comes in the Ω b h 2 constraint. Also, we find that the dark energy equation of state is poorly constrained, while the constraint on the curvature parameter Ω k , shows some improvement when combined with current constraints. When FRBs are combined with future BAO data from 21cm Intensity Mapping (IM), we find little improvement over the constraints from BAOs alone. However, the inclusion of FRBs introduces an additional parameter constraint, Ω b h 2 , which turns out to be comparable to existing constraints. This suggest that FRBs provide valuable information about the cosmological baryon density in the intermediate redshift Universe, independent of high redshift CMB data.

The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaître-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities -density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution. A Details of the LT model construction 31A.1 Finding f and t b 31 A.2 Solving ψ(x) = 0 37 A.3 Limiting values at M = 0 37 A.4 Reconstructing model evolution 38

The dispersion measure -redshift relation of Fast Radio Bursts, DM(z), has been proposed as a potential new probe of the cosmos, complementary to existing techniques. In practice, however, the effectiveness of this approach depends on a number of factors, including (but not limited to) the intrinsic scatter in the data caused by intervening matter inhomogeneities. Here, we simulate a number of catalogues of mock FRB observations, and use MCMC techniques to forecast constraints, and assess which parameters will likely be best constrained. In all cases we find that any potential improvement in cosmological constraints are limited by the current uncertainty on the the diffuse gas fraction, f d (z). Instead, we find that the precision of current cosmological constraints allows one to constrain f d (z), and possibly its redshift evolution. Combining CMB + BAO + SNe + H0 constraints with just 100 FRBs (with redshifts), we find a typical constraint on the mean diffuse gas fraction of a few percent. A detection of this nature would alleviate the "missing baryon problem", and therefore highlights the value of localisation and spectroscopic followup of future FRB detections.