Testing the cosmic distance duality relation with baryon acoustic oscillations and supernovae data

TL;DR

The paper investigates the cosmic distance duality relation (CDDR) by comparing luminosity distances from type Ia supernovae with angular diameter distances from baryon acoustic oscillations, using an artificial neural network (ANN) to match redshifts. It tests three eta(z) parameterizations, $eta(z)=1+eta_0 z$, $eta(z)=1+eta_0 z/(1+z)$, and $eta(z)=1+eta_0 ln(1+z)$, on data from DESI DR2 and SDSS BAO combined with PantheonPlus and DESY5 SN samples, and explores the impact of SN absolute magnitude priors $M_B$. The study finds no evidence for CDDR violation when $M_B$ is treated as a free parameter or when using the $M_B^{B23}$ prior, but a ~2σ deviation arises with the $M_B^{D20}$ prior due to calibration tension with Planck's $r_d$, particularly in the $P_3$ model. Across SDSS+DESY5, DESI+DESY5, and DESI+PantheonPlus datasets, the results are broadly consistent with CDDR, highlighting SN calibration as a dominant systematic in such tests and underscoring the value of high-precision BAO-SN joint analyses for cosmology.

Abstract

One of the most fundamental relationships in modern cosmology is the cosmic distance duality relation (CDDR), which describes the relationship between the angular diameter distance ($D_{\rm A}$) and the luminosity distance ($D_{\rm L}$), and is expressed as: $η(z)=D_{\rm L}(z)(1+z)^{-2}/D_{\rm A}(z)=1$. In this work, we conduct a comprehensive test of the CDDR by combining baryon acoustic oscillation (BAO) data from the SDSS and DESI surveys with type Ia supernova (SN) data from PantheonPlus and DESY5. We utilize an artificial neural network approach to match the SN and BAO data at the same redshift. To explore potential violations of the CDDR, we consider three different parameterizations: (i) $η(z)=1+η_0z$; (ii) $η(z)=1+η_0z/(1+z)$; (iii) $η(z)=1+η_0\ln(1+z)$. Our results indicate that the calibration of the SN absolute magnitude $M_{\rm B}$ plays a crucial role in testing potential deviations from the CDDR, as there exists a significant negative correlation between $η_0$ and $M_{\rm B}$. For PantheonPlus analysis, when $M_{\rm B}$ is treated as a free parameter, no evidence of CDDR violation is found. In contrast, fixing $M_{\rm B}$ to the $M_{\rm B}^{\rm D20}$ prior with $-19.230\pm0.040$ mag leads to a deviation at approximately the $2σ$ level, while fixing $M_{\rm B}$ to the $M_{\rm B}^{\rm B23}$ prior with $-19.396\pm0.016$ mag remains in agreement with the CDDR. Furthermore, overall analyses based on the SDSS+DESY5 and DESI+DESY5 data consistently show no evidence of the deviation from the CDDR.

Figures (5)

• Figure 1: The ANN reconstruction for the SN data. Left panel: The ANN-reconstructed $m_{\rm B}$ for the PantheonPlus over the redshift range $0.01\leq z\leq2.26$. The light green shaded band denotes the $1\sigma$ confidence interval of the ANN reconstruction, while the black points with error bars correspond to the PantheonPlus data points. Right panel: The ANN-reconstructed $\mu$ for the DESY5 over the redshift range $0.025\leq z\leq1.3$. The light red shaded band denotes the $1\sigma$ confidence interval of the ANN reconstruction, and the light grey points with error bars represent the DESY5 data points.
• Figure 2: The triangular plots on $\eta_0$ and $M_{\rm B}$ for the $P_1$ (left panel), $P_2$ (middle panel), and $P_3$ (right panel) models, using SDSS, DESI, and PantheonPlus data.
• Figure 3: The 1D marginalized posterior distributions of the $\eta_0$ parameter for the $P_1$, $P_2$, and $P_3$ models of the CDDR with $M_{\rm B}$ fixed, using $M_{\rm B}^{\rm B23}$ (upper panel) and $M_{\rm B}^{\rm D20}$ (lower panel), based on SDSS, DESI, and PantheonPlus data.
• Figure 4: The 1D marginalized posterior distributions of the $\eta_0$ parameter for the $P_1$, $P_2$, and $P_3$ models of the CDDR, using SDSS, DESI, and DESY5 data.
• Figure 5: The Hubble diagram $D_\mathrm{L}(z)$ and the distance duality ratio $\eta(z)$ from SN and BAO data. Error bars represent the 1$\sigma$ measurement uncertainties. The ratio $\eta(z)$ is expected to be unity, indicated by the dashed line, if the CDDR holds. Notably, because DESY5 covers only a limited redshift range, the resulting $\eta(z)$ data comprise only three points for DESI and four points for SDSS.