Probing Baryonic Feedback and Cosmology with the 3 × 2-point Statistic of Fast Radio Bursts and Galaxies

Abstract The impact of galaxy formation processes on the matter power spectrum is uncertain. Fast radio bursts (FRBs), through their dispersion measures (DMs) encoding the integrated baryon density, offer a unique window into gas distribution. In this work, we investigate the constraining power of a 3 × 2-point correlation statistic of DMs and galaxies. We present the correlation formalism, derive covariance matrices, and forecast signal-to-noise ratios (SNRs) and Fisher constraints. Assuming a host DM variance of 90 pc cm −3 , for 10 4 (10 5 ) FRBs across 35% of the sky, the angular DM power spectrum is noise dominated at multipoles ℓ ≳ 20 (100), implying that the analysis can be conducted using arcminute localizations. In practice, this will be limited by uncertain host associations, which are expected to impact the mean DM subtraction—and thus our assumed value of σ host = 90 pc cm −3 —in DM perturbations. While 10 4 (10 5 ) FRBs can constrain cosmological parameters at the ∼40%–70% (30%–40%) level, this is a factor of ∼2–3 (1.5–2) weaker than the precision attainable with galaxy clustering alone due to shot noise from the FRB number density, variance of the field, and host DMs. On the contrary, feedback-sensitive scales are not currently accessible in galaxy surveys. We demonstrate that combining DM and galaxy correlations in a 3 × 2-point analysis breaks feedback–cosmology degeneracies, yielding ∼10%–18% (7%–13%) precision on cosmological parameters and ∼3% (2%) constraints on feedback using 10 4 (10 5 ) FRBs. For the range of accessible scales, the SNR does not vary significantly with feedback. This work positions the DM–galaxy 3 × 2 point statistic as a promising multiprobe strategy.