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{a}\mathrm{r}\mathrm{c}\mathrm{m}\mathrm{i}\mathrm{n}$$ is sensitive to gas expelled from the halo centre due to galactic feedback. Assuming $20000$ FRBs over $20000{\mathrm{d}\mathrm{e}\mathrm{g}}^2$ with a localisation error being 3 arcmin, we expect that the cross-correlation signal at halo masses of ${10}^{12}-{10}^{14}{M}_{\odot }$ can be measured with a level of $\sim 1\mathrm{\%}$ precision in a redshift range of $0<z<1$. Such precise measurements enable one to put a 1.5% level constraint on $\sigma_8, (\Omega_$\mathrm{M}$/0.3)^{0.5}$anda3\mathrm{\%}levelconstrainton$(\Omega_$\mathrm{b}$/0.049)(h/0.67)(f_$\mathrm{e}$/0.95)$($\sigma_8$,$\Omega_$\mathrm{M}$$,$\Omega_$\mathrm{b}$$,$h$and$f_$\mathrm{e}$$ are the linear mass variance smoothed at $8h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$, 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 $10\mathrm{\%}-20\mathrm{\%}$. Furthermore the cross-correlation analyses can break the degeneracy among ${\mathrm{\Omega }}_{\mathrm{b}}$, $h$ 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.