Testing the cosmic distance-duality relation with localized fast radio bursts: a cosmological model-independent study

TL;DR

The paper addresses the consistency of the Etherington cosmic distance-duality relation by combining SN Ia luminosity distances from Pantheon+ with FRB-based angular diameter distances, using a data-driven ANN ensemble to reconstruct the redshift evolution of the extragalactic dispersion measure without assuming a specific cosmological model.A derivative-based FRB reconstruction links the mean DM_IGM(z) to the expansion history, enabling a model-independent estimation of D_A^{FRB}(z) which is then compared to D_L(z) from SN via η(z) = D_L/[(1+z)^2 D_A], implemented through two covariance-aware likelihoods (direct SN and SN on the FRB grid).Three one-parameter parametrizations of η(z) are tested, and the results show no significant deviation from unity within current uncertainties, with consistent conclusions across both likelihood methods, reinforcing the robustness of the CDDR under this FRB–SN cross-check.The analysis demonstrates a careful treatment of correlated uncertainties arising from global reconstructions and anchors, and sets the stage for stronger tests as localized FRB samples grow, offering a complementary, non-photon-flux-based probe of cosmic geometry.

Abstract

We test the Etherington cosmic distance-duality relation (CDDR), by comparing Type Ia supernova (SNIa) luminosity-distance information from the Pantheon+ compilation with an angular-diameter-distance reconstructed from localized Fast Radio Bursts (FRBs). The core of our methodology is a data-driven reconstruction from FRBs using artificial neural networks (ANNs): we infer a smooth mean extragalactic dispersion-measure relation and use its redshift derivative to recover $H(z)$ and hence $D_\mathrm{A}^{\rm FRB}(z)$ without assuming a parametric form for the expansion history. Possible deviations from CDDR are parameterized through three one-parameter models of $η(z)\equiv D_\mathrm{L}/[(1+z)^2D_\mathrm{A}]$. We implement two complementary likelihoods: (i) a direct approach using individual SNIa with the full Pantheon+ covariance, and (ii) a machine-learning approach in which we reconstruct the SN Hubble diagram on the FRB redshift grid, propagating SN and FRB uncertainties into non-diagonal covariance matrices via Monte Carlo and bootstrap realizations. Within the FRB reconstruction, we anchor the mean extragalactic dispersion measure at $z=0$, which yields a data-driven constraint on the average host/near-source contribution $\mathrm{DM}_{\rm host}=128.8\pm 34.1\,\mathrm{pc\,cm^{-3}}$ ($3σ$ of statistical confidence). We find that both likelihood implementations give consistent posteriors and no statistically significant evidence for departures from CDDR at the current precision.

Figures (5)

• Figure 2: Reconstructed CDDR function $\eta(z)$ for the three parameterizations. Solid lines show posterior medians and shaded regions correspond to the 68% (1$\sigma$) credible intervals. Black dashed line represents $\eta(z)=1$. Method A (FULL) and Method B (ANN) are compared, with results displayed in red and blue, respectively.
• Figure 3: Posterior constraints in the $(\theta,M_\mathrm{B})$ plane for the three $\eta(z)$ families using Method A (FULL). Contours show 68% (1$\sigma$) credible regions; $\theta=\epsilon$ for linear/linfrac and $\theta=\beta$ for power.
• Figure 4: Same as Fig. \ref{['fig:corner_full']}, but for Method B (ANN).
• Figure 5: Distance-space diagnostics for the CDDR comparison (example shown for the power model). The shaded bands show 68% (1$\sigma$) credible intervals. Left: $D_\mathrm{L}(z)$ from SNe compared to $(1+z)^2D_\mathrm{A}^{\rm FRB}(z)\eta(z)$. Right: one-to-one comparison with the $y=x$ line.
• Figure : (a)$\mathrm{DM}_{\mathrm{EG}}(z)$ reconstruction.