A search for the fine-structure constant evolution from fast radio bursts and type Ia supernovae data

The search for a space-time variation of the fundamental constants has been explored over the years to test our physical theories. In this paper, we use the dispersion measure ($DM$) of fast radio bursts (FRB) combined with type Ia supernovae (SNe) data to investigate a possible redshift evolution of the fine-structure constant ($\alpha$), considering the runaway dilaton scenario, which predicts $\frac{\Delta \alpha}{\alpha} = - \gamma\ln{(1+z)}$, where $\gamma$ is a constant proportional to the current value of the coupling between the dilaton field and hadronic matter. We derive all the relevant expressions for the $DM$ dependence concerning the fine-structure constant and constrain the parameter $\gamma$ from measurements of 17 well-localized FRBs and 1048 SNe data from the Pantheon compilation. We also use Monte Carlo simulations to forecast the constraining power of larger samples of FRB measurements for data sets with $N = 500$ and $N = 1000$ points. We found that the uncertainty on $\gamma$ can be improved by one order of magnitude and that limits on $\frac{\Delta \alpha}{\alpha}$ beyond $\sigma \sim 10^{-2}$ will depend crucially on better control of statistical and systematic uncertainties of upcoming FRB data.