Testing the cosmic distance duality relation using Type Ia supernovae and BAO observations

Abstract In this work, we propose to utilize the observed ratio of spherically-averaged distance to the sound horizon scale from Baryon Acoustic Oscillation (BAO) data to test the cosmic distance duality relation (CDDR) by comparing the luminosity distances (LDs) obtained from Type Ia supernovae (SNIa) observations with angular diameter distances (ADDs) derived from these ratio measurements, using a cosmological-model-independent method. To match the LDs with the ADDs at the identical redshifts, we employ two methods: a compressed form of the Pantheon sample and a hybrid approach that combines the binning method with an artificial neural network (ANN). The Hubble parameter H ( z ) at any redshift is reconstructed from the observed Hubble parameter data with the ANN to derive the ADD. To avoid potential biases resulted from the specific prior values of the absolute magnitude $$M_{\textrm{B}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:math> of SNIa and the sound horizon scale $$r_{\textrm{d}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>d</mml:mtext> </mml:msub> </mml:math> from BAO measurements, we introduce the fiducial parameter $$\kappa \equiv 10^{M_{\textrm{B}} \over 5}\, r_{\textrm{d}}^{3 \over 2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>κ</mml:mi> <mml:mo>≡</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mfrac> <mml:msub> <mml:mi>M</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> <mml:mn>5</mml:mn> </mml:mfrac> </mml:msup> <mml:mspace/> <mml:msubsup> <mml:mi>r</mml:mi> <mml:mrow> <mml:mtext>d</mml:mtext> </mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:msubsup> </mml:mrow> </mml:math> and marginalize their impacts by treating them as nuisance parameters with flat prior distributions in our statistical analysis. Subsequently, we update the measurements of ratio of the transverse comoving distance to the sound horizon scale from the latest BAO data released by the Dark Energy Spectroscopic Instrument (DESI) collaboration for CDDR testing. Our results indicate that BAO observation provides a powerful tool for testing the CDDR, independent of both the absolute magnitude $$M_{\textrm{B}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:math> and sound horizon scale $$r_{\textrm{d}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>d</mml:mtext> </mml:msub> </mml:math> , as well as any cosmological model.