Mapping large-scale structure without galaxy formation - combining fast radio bursts with CMB lensing

Fast radio bursts (FRBs) are an emerging precision probe of cosmological fluctuations. The amount and quality of observed FRB data will grow enormously over the next decade. FRB dispersion data directly probe the free electron distribution up to intergalactic scales. Precision models of the free electron distribution are necessary to exploit this exciting new probe of large-scale structure. We show that the free electron distribution almost exactly follows the total matter distribution. We confirm this fact by estimating the electron field-level bias parameters for the first time from the FLAMINGO simulations. With simulation-based knowledge of a handful of electron free parameters, the electron distribution largely acts as a second realization of the matter distribution. Working on large scales, we can leverage this fact to combine FRB correlations with those of Cosmic Microwave Background (CMB) weak lensing to constrain cosmological parameters. Assuming access to localized FRBs with redshifts, we perform cosmological forecasts using these two large-scale matter probes, which have no strong dependence on baryonic feedback models nor on parameters that encode galaxy formation. We show that the parameters $σ_8$ and $Ω_m$ are constrained at a level similar to or better than that obtained by combining FRB dispersion with weak lensing of galaxy shapes under conservative assumptions. These results motivate the use of FRB data as a complementary probe of cosmic structure and will be especially compelling as redshifts become available for localized FRB host galaxies.