Resumo:
Fast radio bursts (FRBs) are a new class of high-energy transient events with short duration within the radio frequency range from a few hundred to a few thousand MHz. Although the physical mechanism responsible for these events is still in debate, the larger value of the observed dispersion measure ($\mathrm{DM}$) above that of the Milk Way contribution suggests an extragalactic or cosmological origin for the FRBs. By identifying the origin of the burst, it is possible to measure the redshift directly and can be combined with $\mathrm{DM}$ to study cosmology. For instance, from the $\mathrm{DM}-z$ relation one can test the weak equivalence principle and constrain the cosmological parameters, such as the fraction of baryon mass in the intergalactic medium ($f_{\mathrm{IGM}}$) and the Hubble constant. Since the first discovered FRB in 2007 by the Parkes telescope, almost one thousand events have been detected by new survey telescopes. However, only a few FRBs in the literature are well localized (with redshift of the host galaxy), and this number is not large enough to perform robust statistical analysis in a cosmological scenario. The other issues in FRB analyses are: (i) the $f_{\mathrm{IGM}}$ is strongly degenerated with the cosmological parameters and is not well constrained; (ii) the poor modeling of the large variance in the $\mathrm{DM}$ due to inhomogeneities in the cosmic electrons density; (iii) and lastly, the limited knowledge of the host galaxy contribution. In this context, in the first part of this Thesis, we discuss in detail the main astrophysical features of FRB. In the second part, dedicated to the cosmological application of FRBs, we present a cosmological model-independent method to estimate the $f_{\mathrm{IGM}}$ and host galaxy contribution by combining FRBs with localized host galaxy and supernovae type Ia dataset. We use the current FRBs observational data and then we explore how future surveys will improve these parameters estimation by simulating the FRBs data from Monte Carlo simulation method. In the second part, we test our physical theories by searching for a space-time variation of the fundamental constants. In particular, we use the dispersion measure of FRBs to investigate a possible redshift evolution of the fine-structure constant ($\alpha$), considering the runaway dilaton scenario. Using a cosmological model-independent method, we derive new expressions for $\mathrm{DM}$ dependence concerning the fine-structure constant.