Probing cosmology and gastrophysics with fast radio bursts: Cross-correlations of dark matter haloes and cosmic dispersion measures

For future surveys of fast radio bursts (FRBs), we clarify information available from cosmic dispersion measures (DMs) through cross-correlation analyses of foreground dark matter haloes (hosting galaxies and galaxy clusters) with their known redshifts. With a halo-model approach, we predict that the cross-correlation with cluster-sized haloes is less affected by the details of gastrophysics, providing robust cosmological information. For less massive haloes, the cross-correlation at angular scales of $<10\, \mathrm{arcmin}$ is sensitive to gas expelled from the halo centre due to galactic feedback. Assuming $20000$ FRBs over $20000 \, {\rm deg}^2$ with a localisation error being 3 arcmin, we expect that the cross-correlation signal at halo masses of $10^{12}-10^{14}\, M_\odot$ can be measured with a level of $\sim 1\%$ precision in a redshift range of $0<z<1$. Such precise measurements enable one to put a 1.5\% level constraint on $\sigma_8\, (\Omega_\mathrm{M}/0.3)^{0.5}$ and a 3\% level constraint on $(\Omega_\mathrm{b}/0.049)(h/0.67)(f_\mathrm{e}/0.95)$ ($\sigma_8$, $\Omega_\mathrm{M}$, $\Omega_\mathrm{b}$, $h$ and $f_\mathrm{e}$ are the linear mass variance smoothed at $8\, h^{-1}\mathrm{Mpc}$, mean mass density, mean baryon density, the present-day Hubble parameter and fraction of free electrons in cosmic baryons today), whereas the gas-to-halo mass relation in galaxies and clusters can be constrained with a level of $10\%-20\%$. Furthermore the cross-correlation analyses can break the degeneracy among $\Omega_\mathrm{b}$, $h$ and $f_\mathrm{e}$, inherent in the DM-redshift relation. Our proposal opens new possibilities for FRB cosmology, while it requires extensive galaxy redshift catalogues and further improvement of the halo model.