Fast radio burst dispersion measure-timing cross-correlations: bias self-calibration and primordial non-Gaussianity constraints

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 $$\propto f_\textrm{NL} H_0^2/k^2$$ ∝ f NL H 0 2 / k 2 dominates, but where cosmic and astrophysical systematic effects are also strongest. A central obstacle to extracting $$f_\textrm{NL}$$ f NL from FRB dispersion measures (DMs) is the degeneracy between the intergalactic-medium (IGM) electron bias $$b_e$$ b e and the primordial non-Gaussianity (PNG) signal, which degrades $$\sigma (f_\textrm{NL})$$ σ ( f NL ) by factors of 1.7–3.3 when $$b_e$$ b e is marginalised, severely limiting the constraining power of any single-bin DM analysis. We introduce a new method to break this degeneracy internally, by exploiting the cross-power spectrum $$C^{D\Delta t}_\ell $$ C ℓ D Δ t between the FRB DM field and the Shapiro timing delays measured along multiple interferometric sightlines. The DM field traces the biased electron density $$\delta _e = b_e\,\delta _m$$ δ e = b e δ m , while the Shapiro timing signal probes the Newtonian gravitational potential $$\Phi \propto -\delta _m/k^2$$ Φ ∝ - δ m / k 2 independently of astrophysical bias. Their cross-correlation, when combined with the timing auto-spectrum as a ratio estimator $$\hat{b}_e(\ell )\equiv C^{D\Delta t}_\ell /C^{\Delta t\Delta t}_\ell $$ b ^ e ( ℓ ) ≡ C ℓ D Δ t / C ℓ Δ t Δ t , isolates $$b_e$$ b e independently of the amplitude of $$P_{mm}$$ P mm , providing a self-calibration of the electron bias from the FRBs. We derive $$C^{D\Delta t}_\ell $$ C ℓ D Δ t analytically in the Limber approximation and demonstrate that corrections to the Limber condition for the timing field are suppressed below $$10^{-6}$$ 10 - 6 at all multipoles of interest, eliminating a potential source of systematic error. A joint Fisher matrix analysis over $$\varvec{\theta } = \{f_\textrm{NL},\,b^0_e,\,z_\textrm{fb}\}$$ θ = { f NL , b e 0 , z fb } , using the complete data vector $$\{C^{DD}_\ell , C^{\Delta t\Delta t}_\ell , C^{D\Delta t}_\ell \}$$ { C ℓ DD , C ℓ Δ t Δ t , C ℓ D Δ t } , shows that including $$C^{D\Delta t}_\ell $$ C ℓ D Δ t reduces $$\sigma (b^0_e)$$ σ ( b e 0 ) by a factor of 2.1–5.1 relative to a DM-only analysis, depending on survey depth and interferometric baseline. After full marginalisation over the bias model, the joint analysis recovers $$\sigma (f_\textrm{NL})$$ σ ( f NL ) within a factor of 1.0–1.9 of the fixed-bias benchmark, compared with a factor of 1.7–3.3 degradation when the cross-spectrum is omitted. While the resulting single-bin forecasts ( $$\sigma (f_\textrm{NL}) \approx 790$$ σ ( f NL ) ≈ 790 –1360 for $$N_\textrm{FRB} = 10^4$$ N FRB = 10 4 , $$l = 500\,\textrm{AU}$$ l = 500 AU ) remain weaker than current large-scale structure constraints ( $$\sigma (f_\textrm{NL}) \approx 20$$ σ ( f NL ) ≈ 20 –50 from galaxy clustering), this paper is primarily a methodological contribution: we establish $$C^{D\Delta t}_\ell $$ C ℓ D Δ t as a new, internally self-calibrated observable for FRB surveys, and provide the Fisher machinery needed to incorporate it into future tomographic analyses.