New tests of the cosmic distance duality relation with the baryon acoustic oscillation and type Ia supernovae

The cosmic distance duality relation (CDDR), η(z)≡(1+z)-2DL/DA=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta (z)\equiv (1+z)^{-2}D_{\mathrm{{L}}}/D_{\mathrm{{A}}}=1$$\end{document}, plays a fundamental role in cosmology and astronomy since any violation of CDDR could be a signal of new physics. In this paper, we re-test the validity of CDDR by using the newest baryon acoustic oscillations (BAO) measurements from baryon oscillation spectroscopic survey data release 12 and the latest Pantheon type Ia supernovae (SNIa) sample. Using three parameterizations of η(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta (z)$$\end{document}, namely η(z)=1+η1z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta (z)=1+\eta _1 z$$\end{document}, η(z)=1+η2z1+z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta (z)=1+\eta _2 \frac{z}{1+z}$$\end{document} and η(z)=1+η3ln(1+z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta (z)=1+\eta _3\mathrm{ln}(1+z)$$\end{document}, and considering the effects of the uncertainty of dimensionless Hubble constant h, we find that the CDDR is valid at 1σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\sigma $$\end{document} confidence level (CL) whether h is free or marginalized over with a flat prior distribution. However, when marginalizing over h with two different Gaussian distributions, we find that the CDDR is valid at 2σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\sigma $$\end{document} CL with h=0.6727±0.0060\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h=0.6727\pm 0.0060$$\end{document}, while it is valid only at 4σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\sigma $$\end{document} CL with h=0.7403±0.0142\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h=0.7403\pm 0.0142$$\end{document}. Our results show that although using the newest BAO measurements and Pantheon SNIa sample can significantly improve the accuracy of η(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta (z)$$\end{document}, more precise data points of angular diameter distance and luminosity distance as well as accurate measurement of h are needed to test the validity of CDDR.