Probing the Distance Duality Relation with Machine Learning and Recent Data

TL;DR

This paper tests the distance duality relation (DDR) using the latest supernova and BAO data, employing both a parametric $\eta(z)=(1+z)^\varepsilon$ framework and a model-independent genetic algorithm (GA) reconstruction. The analysis reveals that when Cepheid calibration and BBN priors are included, the DDR appears violated in the parametric approach, largely reflecting the underlying Hubble tension between high- and low-redshift probes; in contrast, the GA generally finds no significant DDR deviation. The results depend sensitively on data combinations and calibration choices, underscoring the importance of model-independent DDR tests to avoid artefacts from parametric bias. Overall, the work clarifies how current tensions in $H_0$ propagate into DDR constraints and demonstrates the value of nonparametric approaches for robust cosmological consistency tests.

Abstract

The distance duality relation (DDR) relates two independent ways of measuring cosmological distances, namely the angular diameter distance and the luminosity distance. These can be measured with baryon acoustic oscillations (BAO) and Type Ia supernovae (SNe Ia), respectively. Here, we use recent DESI DR1, Pantheon+, SH0ES and DES-SN5YR data to test this fundamental relation. We employ a parametrised approach and also use model-independent Generic Algorithms (GA), which are a machine learning method where functions evolve loosely based on biological evolution. When we use DESI and Pantheon+ data without Cepheid calibration or big bang nucleosynthesis (BBN), there is a $2σ$ violation of the DDR in the parametrised approach. Then, we add high-redshift BBN data and the low-redshift SH0ES Cepheid calibration. This reflects the Hubble tension since both data sets are in tension in the standard cosmological model $Λ$CDM. In this case, we find a significant violation of the DDR in the parametrised case at $6σ$. Replacing the Pantheon+ SNe Ia data by DES-SN5YR, we find similar results. For the model-independent approach, we find no deviation in the uncalibrated case and a small deviation with BBN and Cepheids which remains at 1$σ$. This shows the importance of considering model-independent approaches for the DDR.

Figures (11)

• Figure 1: Illustration of GA operations.
• Figure 2: $\chi^2$ of the GA functions per generation for the standard DESI+Pantheon+ case.
• Figure 3: Evaluation of the profile likelihood of $\Omega_\mathrm{m}\xspace$ and $\epsilon$ with Pantheon+ and DESI DR1 data for different cases.
• Figure 4: Contour plot of $h$ and $\epsilon$ for Pantheon+SH0ES (yellow), DESI+BBN (blue) and their combination (red).
• Figure 5: Contour plot of $\Omega_\mathrm{m}\xspace$ and $\epsilon$ for Pantheon+SH0ES (yellow), DESI+BBN (blue) and their combination (red) using only the comoving distance measurements $d_{\rm M}$ from DESI.