A hydrodynamical simulations-based model that connects the FRB DM--redshift relation to suppression of the matter power spectrum via feedback

Understanding the impact of baryonic feedback on the small-scale ($k \gtrsim 1\,h\,$Mpc$^{-1}$) matter power spectrum is a key astrophysical challenge, and essential for interpreting data from upcoming weak-lensing surveys, which require percent-level accuracy to fully harness their potential. Astrophysical probes, such as the kinematic and thermal Sunyaev-Zel'dovich effects, have been used to constrain feedback at large scales ($k \lesssim 5\,h\,$Mpc$^{-1}$). The sightline-to-sightline variance in the fast radio bursts (FRBs) dispersion measure (DM) correlates with the strength of baryonic feedback and offers unique sensitivity at scales upto $k \sim 10\,h\,$Mpc$^{-1}$. We develop a new simulation-based formalism in which we parameterize the distribution of DM at a given redshift, $p(\mathrm{DM}|z)$, as a log-normal with its first two moments computed analytically in terms of cosmological parameters and the feedback-dependent electron power spectrum $P_\mathrm{ee}(k, z)$. We find that the log-normal parameterization provides an improved description of the $p(\mathrm{DM}|z)$ distribution observed in hydrodynamical simulations as compared to the standard $F$-parameterization. Our model robustly captures the baryonic feedback effects across a wide range of baryonic feedback prescriptions in hydrodynamical simulations, including IllustrisTNG, SIMBA and Astrid. Leveraging simulations incorporates the redshift evolution of the DM variance by construction and facilitates the translation of constrained feedback parameters to the suppression of matter power spectrum relative to gravity-only simulations. We show that with $10^4$ FRBs, the suppression can be constrained to percent-level precision at large scales and $\sim 10$\% precision at scales $k \gtrsim 10\,h\,$Mpc$^{-1}$ with prior-to-posterior $1σ$ constraint width ratio $\gtrsim 20$.