Abstract
The column density of free electrons with a cosmological-scale depth, cosmic
dispersion measures (DMs), is among the most interesting observables in future
transient surveys at radio wavelengths. For future surveys of fast radio bursts
(FRBs), we clarify information available from cosmic 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 $<10\,
arcmin$ is sensitive to gas expelled from the halo centre due to
galactic feedback. Assuming $20000$ FRBs over $20000 \, deg^2$ with a
localisation error being 3 arcmin, we expect that the cross-correlation signal
at halo masses of $10^12$-$10^14\, M_ødot$ can be measured with a level of
$1\%$ precision in a redshift range of $0<z<1$. Such precise measurements
enable to put a $1.5\%$ level constraint on $\sigma_8\,
(Ømega_M/0.3)^0.5$ and a $3\%$ level constraint on
$(Ømega_b/0.049)(h/0.67)(f_e/0.95)$ ($\sigma_8$,
$Ømega_M$, $Ømega_b$, $h$ and $f_e$ are the linear
mass variance smoothed at $8\, h^-1Mpc$, 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 $Ømega_b$,
$h$ and $f_e$, inherent in the DM-redshift relation.
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