Revisiting Cosmic Distance Duality with Megamasers and DESI DR2 Observations: Model Independent Constraints on Early-Late Calibration

TL;DR

This work probes the Cosmic Distance Duality Relation (CDDR) η(z) ≡ $d_L(z)/[(1+z)^2 d_A(z)]$ across cosmic time by combining calibration-free Megamaser angular diameter distances with Pantheon+ Type Ia SNe, and by using DESI DR2 BAO distances in tandem with SNIa data. It demonstrates that BAO+SNIa tests are highly sensitive to the early-late calibration pair $(r_d, M_b)$, with a degeneracy that can be broken by adding Megamaser distances, yielding model-independent constraints on the calibrations under the assumption η(z)=1. The study reports current constraints $r_d=137.5\pm5$ Mpc and $M_b=-19.3\pm0.08$, and shows that future data from LSST SNIa and MCP Megamasers could substantially tighten these bounds to about $\sigma_{M_b}\approx0.04$ and $\sigma_{r_d}\approx2.5$ Mpc. Overall, the results affirm CDDR consistency within uncertainties while highlighting the critical role of calibration-free probes for robustly constraining early–late cosmic calibrations and informing the cosmic calibration tension related to $H_0$.

Abstract

The Cosmic Distance Duality Relation (CDDR) connects the angular diameter distance ($d_A$) and the luminosity distance ($d_L$) at a given redshift. This fundamental relation holds in any metric theory of gravity, provided that photon number is conserved and light propagates along null geodesics. A deviation from this relation could indicate new physics beyond the standard cosmological model. In this work, we test the validity of the CDDR at very low redshifts ($z < 0.04$) by combining $d_A$ from the Megamaser Cosmology Project with $d_L$ from the Pantheon+ sample of Type Ia Supernovae (SNIa). We further incorporate high-redshift Baryon Acoustic Oscillation (BAO)-based $d_A$ measurements from DESI DR2 in combination with SNIa data, highlighting the critical role of the $r_d-M_b$ (early-late) calibration in testing the CDDR using these two probes. Assuming CDDR holds, we perform a Bayesian analysis to derive model-independent constraints on the calibration parameters. Using only BAO and SNIa data, we observe a strong degeneracy between $r_d$ and $M_b$. However, the inclusion of calibration-free Megamaser measurements breaks this degeneracy, enabling independent constraints without relying on a specific cosmological model or distance-ladder techniques. Additionally, we present a forecast incorporating the expected precision from future Megamaser and SNIa observations, demonstrating their potential to significantly tighten constraints on early-late calibration parameters, under the assumption of validity of CDDR.

Figures (4)

• Figure 1: The distance duality ratio $\eta(z)$ obtained using reconstructed $d_L$ from SNIa and $d_A$ from Megamaser data Pesce:2020xfe. Error bars represent the $1\sigma$ measurement uncertainties, incorporating contributions from both SNIa and Megamaser data. The ratio $\eta(z)$ is expected to be unity, indicated by the dashed line, if CDDR holds. The supernova distances are computed using $M_b = -19.25$, though the resulting $\eta(z)$ remains consistent with unity under small variations in $M_b$.
• Figure 2: The distance duality ratio $\eta(z)$ obtained using reconstructed $d_L$ from SNIa and $d_A$ from DESI BAO data DESI:2025zgx, for different choices of calibration parameters. Error bars represent the $1\sigma$ measurement uncertainties, incorporating contributions from both SNIa and BAO data. The ratio $\eta(z)$ is expected to be unity, indicated by the dashed line, if CDDR holds.
• Figure 3: Constraints (left) and forecast (right) for the calibration parameters assuming the validity of CDDR. Colors for 1D and 2D posteriors represent the datasets used in combination with Pantheon+ SNIa. The vertical bands in the left panel show constraints on $r_d$ and $M_b$ from Planck18+$\Lambda$CDM and SH0ES collaboration, respectively. The inclusion of Megamaser data, alongside DESI BAO and Pantheon+, breaks the $r_d-M_b$ degeneracy.
• Figure 4: Gaussian Process reconstruction of the luminosity distance $d_L(z)$ using the Pantheon+ SNIa for $M_b=-19.25$. Black points represent binned data points, while the brown solid line indicates the GPR mean prediction. The shaded regions correspond to 1$\sigma$ and 2$\sigma$ uncertainty bands.