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Testing the Distance-Duality Relation from Hubble, Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

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Abstract

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D L(1+z)−2/D A by combining the angular diameter distance D A(or comoving distances D c ) with the luminosity distance D L. The D A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D c are obtained from Hubble parameter data and D L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z−z SNe|<0.005, and method B: reconstructing the D L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D L associated with the redshits of the observed D A or D c. Four parameterizations for η(z), i.e., η(z)=1+η 0 z, η(z)=1+η 0 z/(1+z), η(z)=1+η 0 z/(1+z)2 and η(z)=1−η 0 ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.

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Acknowledgments

We thank the anonymous referees and Prof. Punxun Wu and Mr. Zhengxiang Li for constructive suggestions and comments. This work was supported by the National Natural Science Foundation of China under Grant Nos. 10935013, 11147011, 11222545, 11175093 and 11075083, the Science Research Fund of Hunan Provincial Education Department No. 11B050, the Hunan Provincial Natural Science Foundation of China under Grant No. 12JJA001, the Zhejiang Provincial Natural Science Foundation of China under Grant Nos. Z6100077 and R6110518, the SRFDP under Grant No. 20124306110001, the FANEDD under Grant No. 200922, the National Basic Research Program of China under Grant No. 2010CB832803 and the NCET under Grant No. 09-0144.

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  1. Institute of Physics, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, China

    Zhaoxia Chen, Bingju Zhou & Xiangyun Fu

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  1. Zhaoxia Chen
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  2. Bingju Zhou
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  3. Xiangyun Fu
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Correspondence to Bingju Zhou.

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Chen, Z., Zhou, B. & Fu, X. Testing the Distance-Duality Relation from Hubble, Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods. Int J Theor Phys 55, 1229–1240 (2016). https://doi.org/10.1007/s10773-015-2765-1

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  • DOI: https://doi.org/10.1007/s10773-015-2765-1

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