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Testing the cosmic distance duality relation using model-independent approach

Shubham Barua, Sujit K. Dalui, Rikiya Okazaki, Shantanu Desai

TL;DR

This work advances a model-independent test of the cosmic distance duality relation $D_L(z)=(1+z)^2 D_A(z)$ by applying an arbitrary-pivot Padé-(2,1) expansion to constrain cosmography at fixed redshifts $z_0$. Using DESI BAO with $r_d$ prior, Cosmic Chronometers, and Type Ia SNe from PantheonPlus and DESY5, it derives $D_A(z_0)$, $D_L(z_0)$, and the pivoted CDDR factor $\eta(z_0)=\frac{D_L(z_0)}{(1+z_0)^2 D_A(z_0)}$, avoiding extrapolation of low-$z$ constraints. The results show no CDDR violation within $1\sigma$ for uncalibrated datasets, but a $3$–$5\sigma$ tension arises when a Gaussian prior on $M_B$ is imposed, reflecting a tension between early- and late-universe calibrations. Overall, the arbitrary-pivot Padé approach provides a robust, redshift-specific, model-independent framework for testing fundamental distance dualities and can be extended to higher redshifts as data improve.

Abstract

In this work, we test the cosmic distance duality relation (CDDR) using the arbitrary redshift pivot Padé-(2,1) expansion methodology developed in arXiv:2509.16196. This approach allows us to constrain cosmography parameters and test CDDR at any redshift. Further, it does not rely on data reconstructions or extrapolations of the cosmography parameters to higher redshifts. We employ observational data from the Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation dataset, cosmic chronometers (CC), and Type Ia supernovae from the Pantheon Plus (PP) and Dark Energy Survey Year 5 (DESY5) compilations. We find no significant deviations from the standard CDDR relation in the range $0\lesssim z \lesssim 1$ when considering DESI$+r_d$ dataset in combination with PP$+$CC and DESY5$+$CC datasets. However, on imposing a Gaussian prior on $M_B \in \mathcal{N}(-19.253, 0.027)$ (instead of treating it as a free parameter) in the dataset combination PP$+$CC, we find CDDR violation at a level of $(3-5)σ.$

Testing the cosmic distance duality relation using model-independent approach

TL;DR

This work advances a model-independent test of the cosmic distance duality relation by applying an arbitrary-pivot Padé-(2,1) expansion to constrain cosmography at fixed redshifts . Using DESI BAO with prior, Cosmic Chronometers, and Type Ia SNe from PantheonPlus and DESY5, it derives , , and the pivoted CDDR factor , avoiding extrapolation of low- constraints. The results show no CDDR violation within for uncalibrated datasets, but a – tension arises when a Gaussian prior on is imposed, reflecting a tension between early- and late-universe calibrations. Overall, the arbitrary-pivot Padé approach provides a robust, redshift-specific, model-independent framework for testing fundamental distance dualities and can be extended to higher redshifts as data improve.

Abstract

In this work, we test the cosmic distance duality relation (CDDR) using the arbitrary redshift pivot Padé-(2,1) expansion methodology developed in arXiv:2509.16196. This approach allows us to constrain cosmography parameters and test CDDR at any redshift. Further, it does not rely on data reconstructions or extrapolations of the cosmography parameters to higher redshifts. We employ observational data from the Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation dataset, cosmic chronometers (CC), and Type Ia supernovae from the Pantheon Plus (PP) and Dark Energy Survey Year 5 (DESY5) compilations. We find no significant deviations from the standard CDDR relation in the range when considering DESI dataset in combination with PPCC and DESY5CC datasets. However, on imposing a Gaussian prior on (instead of treating it as a free parameter) in the dataset combination PPCC, we find CDDR violation at a level of
Paper Structure (4 sections, 8 equations, 1 figure, 1 table)

This paper contains 4 sections, 8 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results and Discussion
  4. Conclusions

Figures (1)

  • Figure 1: Constraints on $\eta(z_0)$ along with 68% credible intervals for SNe$+$CC dataset (where SNe is either PP or DESY5) in combination with BAO$+r_d$ at the pivot redshifts $z_0\in[0,1]$.