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A geometric measure of dark energy with pairs of galaxies


Observations1,2 indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity3,4. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance () and equation of state () of dark energy5. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement6,7,8,9,10,11,12,13,14,15,16,17,18. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data19,20. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at and the dark energy equation-of-state parameter at , and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and .

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Figure 1: Geometry and statistics of binary galactic systems.
Figure 2: Diagram of the average anisotropy of pairs from the SDSS (Data Release 7) 19 and DEEP2 20 data.
Figure 3: Cosmological constraints on the abundance of dark energy ΩX and on its nature .


  1. Riess, A. et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)

    ADS  Article  Google Scholar 

  2. Perlmutter, S. et al. Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999)

    ADS  Article  Google Scholar 

  3. Peebles, P. J. E. & Ratra, B. The cosmological constant and dark energy. Rev. Mod. Phys. 75, 559–606 (2003)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  4. Frieman, J. A., Turner, M. S. & Huterer, D. Dark energy and the accelerating universe. Annu. Rev. Astron. Astrophys. 46, 385–432 (2008)

    ADS  CAS  Article  Google Scholar 

  5. Alcock, C. & Paczyski, B. An evolution free test for non-zero cosmological constant. Nature 281, 358–359 (1979)

    ADS  Article  Google Scholar 

  6. Kim, Y.-R. & Croft, R. A. C. A potentially pure test of cosmic geometry: galaxy clusters and the real space Alcock-Paczynski test. Mon. Not. R. Astron. Soc. 374, 535–546 (2007)

    ADS  CAS  Article  Google Scholar 

  7. Ryden, B. S. Measuring q0 from the distortions of voids in redshift space. Astrophys. J. 452, 25–32 (1995)

    ADS  Article  Google Scholar 

  8. Ryden, B. S. & Melott, A. Voids in real space and in redshift space. Astrophys. J. 470, 160–171 (1996)

    ADS  Article  Google Scholar 

  9. Phillips, S. A possible geometric measurement of the cosmological constant. Mon. Not. R. Astron. Soc. 269, 1077–1081 (1994)

    ADS  Article  Google Scholar 

  10. Matsubara, T. & Suto, Y. Cosmological redshift distortion of correlation functions as a probe of the density parameter and the cosmological constant. Astrophys. J. 470, 1–5 (1996)

    ADS  Article  Google Scholar 

  11. Ballinger, W. E., Peacock, J. & Heavens, A. F. Measuring the cosmological constant with redshift surveys. Mon. Not. R. Astron. Soc. 282, 877–888 (1996)

    ADS  CAS  Article  Google Scholar 

  12. Popowski, P. A., Weinberg, D. H., Rayden, B. S. & Osmer, P. Quasar clustering and spacetime geometry. Astrophys. J. 498, 11–25 (1998)

    ADS  Article  Google Scholar 

  13. Hui, L., Stebbins, A. & Burles, S. A geometrical test of the cosmological energy contents using the Ly-α forest. Astrophys. J. 511, 5–8 (1999)

    ADS  Article  Google Scholar 

  14. McDonald, P. Toward a measurement of the cosmological geometry at z 2: Predicting Lyα forest correlation in three dimensions and the potential of future data. Astrophys. J. 585, 34–51 (2003)

    ADS  Article  Google Scholar 

  15. da Angela, J., Outram, P. J. & Shanks, T. Constraining β(z) and Ω m0 from redshift-space distortions in z3 galaxy surveys. Mon. Not. R. Astron. Soc. 361, 879–886 (2005)

    ADS  Article  Google Scholar 

  16. Nusser, A. The Alcock-Paczynski test in redshifted 21-cm maps. Mon. Not. R. Astron. Soc. 364, 743–750 (2005)

    ADS  CAS  Article  Google Scholar 

  17. Barkana, R. Separating out the Alcock-Paczynski effect on 21-cm fluctuations. Mon. Not. R. Astron. Soc. 372, 259–264 (2006)

    ADS  CAS  Article  Google Scholar 

  18. Mc Quinn, M. et al. Cosmological parameter estimation using 21cm radiation from the epoch of reionisation. Astrophys. J. 653, 815–834 (2006)

    ADS  CAS  Article  Google Scholar 

  19. Abazajian, K. N. et al. The seventh data release of the Sloan Digital Sky Survey. Astrophys. J. Suppl. Ser. 182, 543–558 (2009)

    ADS  Article  Google Scholar 

  20. Davis, M. et al. The All-Wavelength Extended Groth Strip International Survey (AEGIS) data sets. Astrophys. J. 660, 1–4 (2007)

    ADS  Article  Google Scholar 

  21. Strauss, M. A. & Willick, J. A. The density and peculiar velocity fields of nearby galaxies. Phys. Rep. 261, 271–431 (1995)

    ADS  Article  Google Scholar 

  22. Marinoni, C. et al. Galaxy distances in the nearby Universe: corrections for peculiar motions. Astrophys. J. 505, 484–505 (1998)

    ADS  Article  Google Scholar 

  23. Marinoni, C., Bel, J. & Buzzi, A. The scale of cosmic isotropy. Phys. Rev. Lett. (submitted)

  24. Coil, A. et al. The DEEP2 Galaxy Redshift Survey: clustering of galaxies in early data. Astrophys. J. 609, 525–538 (2004)

    ADS  CAS  Article  Google Scholar 

  25. Kessler, R. et al. First year SDSSII supernovae results: Hubble diagram and cosmological parameters. Astrophys. J. Suppl. Ser. 185, 32–84 (2009)

    ADS  CAS  Article  Google Scholar 

  26. Astier, P. et al. The Supernovae Legacy Survey: measurement of Ωm, ΩΛand w from the first data set. Astron. Astrophys. 447, 31–48 (2006)

    ADS  Article  Google Scholar 

  27. Dunkley, J. et al. Five-year Wilkinson Microwave Anisotropy Probe observations: likelihoods and parameters from the WMAP data. Astrophys. J. Suppl. Ser. 180, 306–329 (2009)

    ADS  CAS  Article  Google Scholar 

  28. Eisenstein, D. J. et al. Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies. Astrophys. J. 633, 560–574 (2005)

    ADS  Article  Google Scholar 

  29. Percival, W. et al. Baryon acoustic oscillations in the Sloan Digital Sky Survey Data Release 7 galaxy sample. Mon. Not. R. Astron. Soc. 401, 2148–2168 (2010)

    ADS  Article  Google Scholar 

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C.M. thanks J. Bel, P.-E. Crouzet, M. Davis, L. Guzzo, A. Blanchard, E. Branchini, P. S. Corasaniti, A. Ealet, A. Heavens, O. Le Fèvre, L. Moscardini, T. Schucker, P. Taxil and J. M. Virey for discussions. We thank R. Giovanelli, L. Lellouch and P. J. Morrison for reading versions of the manuscript. This paper has greatly benefited from the comments of M. Strauss. C.M. is grateful for support from the Projets Exploratoires Pluridisciplinaires: Physique Théorique et ses Interfaces of the CNRS and from specific project funding of the Institut Universitaire de France.

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Authors and Affiliations



C.M elaborated the testing formalism. C.M. and A.B. worked on the comparison of theoretical predictions with observations.

Corresponding author

Correspondence to Christian Marinoni.

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The authors declare no competing financial interests.

Additional information

The posterior likelihood shown in Fig. 3 is available at

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Supplementary Information

The file contains Supplementary Text and Data I-VI, additional references, Supplementary Table 1 and Supplementary Figures 1-5 with legends. (PDF 1200 kb)

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Marinoni, C., Buzzi, A. A geometric measure of dark energy with pairs of galaxies. Nature 468, 539–541 (2010).

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