Testing the cosmic distance duality relation using model-independent approach

Abstract In this work, we test the cosmic distance duality relation (CDDR) using the arbitrary redshift pivot Padé-(2,1) expansion methodology developed in Ref Fazzari et al. http://arxiv.org/abs/2509.16196 . This approach allows us to constrain the cosmography parameters and test the 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 $$0\lesssim z \lesssim 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≲</mml:mo> <mml:mi>z</mml:mi> <mml:mo>≲</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> when considering DESI $$+r_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:mrow> </mml:math> dataset in combination with PP+CC and DESY5+CC datasets. However, on imposing a Gaussian prior on $$M_B \in \mathcal {N}(-19.253, 0.027)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>B</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mn>19.253</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0.027</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> (instead of treating it as a free parameter) in the dataset combination PP+CC, we find CDDR violation at a level of $$(3-5)\sigma .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:math>