The One-Loop Power Spectrum of Fast Radio Burst Dispersion Measures

Abstract

Fast radio burst (FRB) dispersion measures trace free electron column densities and will soon offer a unique probe of low-$z$ baryons. Such measurements can constrain cosmology directly, with the free electrons serving as a new tracer of large-scale structure, and probe the baryonic feedback of galaxies, a leading systematic for weak lensing surveys such as LSST and Euclid. We prepare for both science cases using effective field theory (EFT) and hydrodynamical simulations. We construct the one-loop EFT description of the free-electron auto-spectrum $P_{ee}$ and electron-galaxy cross-spectrum $P_{eg}$, placing FRB dispersion clustering on the same theoretical footing as spectroscopic galaxy analyses, and quantify the FRB densities at which this modeling is useful. We also investigate suitable galaxy samples for cross-correlations, finding that current spectroscopic catalogs provide appropriate redshift range and sufficient density. We validate the model against the FLAMINGO simulations, jointly fitting $P_{ee}$, $P_{eg}$, and $P_{gg}$ for DESI-like samples at $z=0.2$ and 0.5. The model describes all three spectra to $k\sim0.2\,h\,{\rm Mpc}^{-1}$, with an electron linear bias $b_{e,1}\simeq0.92$, higher-order biases consistent with zero, and all parameters stable across feedback variants. Together with the near-perfect electron-matter correlation $r_{em}\simeq1$, this establishes free electrons as nearly unbiased, feedback-robust tracers of matter, supporting a key assumption of FRB-based feedback constraints. These properties make electron clustering an ideal application for Hybrid Effective Field Theory (HEFT), which would extend the modeling reach by a further factor of 2--3. The low-$z$ electron spectrum becomes signal-dominated beyond the linear regime within the first few years of next-generation surveys; the models developed here will be necessary on these timescales.