Fast Radio Burst Dispersion Measure--Timing Cross-Correlations: Bias Self-Calibration and Primordial Non-Gaussianity Constraints

Abstract

Fast Radio Bursts (FRBs) carry fossil information about non-Gaussianity generated during inflation. This primordial signal is most accessible on the largest scales, where the scale-dependent bias correction $\propto f_\mathrm{NL}\,H_0^2/k^2$ dominates, but where systematic effects are also strongest. A central challenge is the degeneracy between the intergalactic-medium electron bias $b_e$ and the primordial non-Gaussianity (PNG) signal, which can degrade $\sigma(f_\mathrm{NL})$ by orders of magnitude when $b_e$ is marginalised. We show this degeneracy can be broken internally by exploiting the cross-power spectrum $C_\ell^{D\Delta t}$ between the FRB dispersion measure (DM) field and Shapiro timing delays along multiple interferometric sightlines. The DM field traces the biased electron density, while the Shapiro timing signal probes the Newtonian gravitational potential independently of astrophysical bias. Their cross-correlation is directly proportional to $b_e$, independently of the matter power spectrum, providing a self-calibration of the electron bias. We derive $C_\ell^{D\Delta t}$ analytically in the Limber approximation and find a correlation coefficient $|\rho(\ell)|\approx 0.51$--$0.79$ across $\ell = 2$--$100$. A joint Fisher matrix analysis over $\{f_\mathrm{NL},\,b_e^0,\,z_\mathrm{fb}\}$ shows that including the cross-spectrum reduces $\sigma(b_e^0)$ by a factor of $2.1$--$5.1$ relative to a DM-only analysis. After full marginalisation, the joint analysis recovers $\sigma(f_\mathrm{NL})$ within a factor of $1.0$--$1.9$ of the fixed-bias benchmark, compared with $1.7$--$3.3$ degradation without the cross-spectrum. For a shallow survey with a 500\,AU baseline and $10^4$ FRBs, the joint constraint achieves $\sigma(f_\mathrm{NL})\approx 790$, within 4\% of the fixed-bias result and a factor $3.3$ better than the marginalised DM-only case.