We demonstrated that the models with α = 1 2 predict the de- viation from a simple power-law scaling in the S ( M ) rela- tion. Comparison of predictions of such models with the data, collected in [14] potentially allows to restrict the values of r$_{c}$ from below for a given α . The improved data-processing and new observational data on DM distributions will allow to strengthen these bounds and make them quantitative. In this work we have analyzed only the case when the turn- around sphere is well inside the Vainstein radius, r$_{V}$ ≫ R$_{ta}$ . To analyze a general case, a better theoretical understanding of the function π ( r ) (defined via Eq. (5)) is needed. Together with better quality of data this will allow to extend our analy- sis to a wider range of parameters. In the case α = 1 2 (the DGP model) the S ( M ) dependence remains featureless. In this case one has r$_{V}$ ≈ R$_{ta}$ for all masses (for r$_{c}$ ∼ H − 1 0 ) and the deviations from the Newto- nian gravity at turn-around radius will be strong. Therefore this model (in general, all models that have r$_{V}$ ∼ R$_{ta}$ for ha- los of M ∼ 10 $^{12}$M $_{⊙}$) can be probed by studying the infall trajectories around the turn-around radius in the Local Group and nearby galaxies [29] using the available data and the data from forthcoming surveys of the Milky Way as well as GAIA mission. Acknowledgments. We would like to thank G. Dvali for many useful and illuminating discussions and careful reading of the manuscript. This work was supported in part by the Swiss National Science Foundation. 4 Another way to probe the S − M relation for general r$_{c}$ and α is to do numerical simulations in the theories of modified gravity (see examples in [11, 12]) and compare directly with observations both the scaling of the central values of S and M and the scatter around it. Conclusion. The main purpose of this work was to iden- tify a new observable that can be used to constrain the large scale modifications of gravity. We see that the scaling prop- erties of dark matter halos are sensitive to such modificatio ns. FIG. 4: Range of r c for which r V ≈ R ta for some halo masses in the range 10 − 10 $^{15}$M ⊙ . [1] G. R. Dvali, G. Gabadadze, and M. Porrati, Phys. Lett. B485 , 208 (2000), hep-th/0005016. [2] C. Deffayet, G. R. Dvali, and G. Gabadadze, Phys. Rev. D65 , 044023 (2002), astro-ph/0105068. [3] G. Dvali, New J. Phys. 8 , 326 (2006), hep-th/0610013. [4] G. Dvali, S. Hofmann, and J. Khoury, Phys. Rev. D76 , 084006 (2007), hep-th/0703027. [5] G. Dvali, to appear (2010). [6] G. Dvali, A. Gruzinov, and M. Zaldarriaga, Phys. Rev. D68 , 024012 (2003), hep-ph/0212069. [7] G. Dvali and M. S. Turner (2003), astro-ph/0301510. [8] J. Sollerman et al., Astrophys. J. 703 , 1374 (2009), 0908.4276. [9] L. Lombriser, W. Hu, W. Fang, and U. Seljak, Phys. Rev. D80 , 063536 (2009), 0905.1112. [10] R. Scoccimarro, Phys. Rev. D80 , 104006 (2009), 0906.4545. [11] K. C. Chan and R. Scoccimarro, Phys. Rev. D80 , 104005 (2009), 0906.4548. [12] J. Khoury and M. Wyman, Phys. Rev. D80 , 064023 (2009), 0903.1292. [13] A. Boyarsky, A. Neronov, O. Ruchayskiy, and I. Tkachev (2009), 0911.3396. [14] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, A. V. Maccio’, and D. Malyshev (2009), 0911.1774. [15] J. Kormendy and K. C. Freeman, in Dark Matter in Galax- ies , edited by S. Ryder, D. Pisano, M. Walker, & K. Freeman (2004), vol. 220 of IAU Symposium , p. 377. [16] F. Donato, G. Gentile, P. Salucci, C. Frigerio Martins, M. I. Wilkinson, G. Gilmore, E. K. Grebel, A. Koch, and R. Wyse, MNRAS 397 , 1169 (2009), 0904.4054. [17] G. Gentile, B. Famaey, H. Zhao, and P. Salucci, Nature 461 , [18] A. V. Macci`o, A. A. Dutton, and F. C. van den Bosch, MNRAS 391 , 1940 (2008), 0805.1926. [19] V. Springel, J. Wang, M. Vogelsberger, A. Ludlow, A. Jenkins, A. Helmi, J. F. Navarro, C. S. Frenk, and S. D. M. White, MN- RAS 391 , 1685 (2008), 0809.0898. [20] C. Deffayet, G. R. Dvali, G. Gabadadze, and A. I. Vainshtein, Phys. Rev. D65 , 044026 (2002), hep-th/0106001. [21] J. F. Navarro, C. S. Frenk, and S. D. M. White, ApJ 490 , 493 (1997), astro-ph/9611107. [22] A. Burkert, ApJ 447 , L25+ (1995), arXiv:astro-ph/9504041. [24] D. A. Buote, F. Gastaldello, P. J. Humphrey, L. Zappacosta, J. S. Bullock, F. Brighenti, and W. G. Mathews, ApJ 664 , 123 (2007), arXiv:astro-ph/0610135. [23] A. Vikhlinin, A. Kravtsov, W. Forman, C. Jones, M. Marke- vitch, S. S. Murray, and L. Van Speybroeck, ApJ 640 , 691 (2006), astro-ph/0507092. [25] R. W. Schmidt and S. W. Allen, MNRAS 379 , 209 (2007), arXiv:astro-ph/0610038. [26] J. M. Comerford and P. Natarajan, MNRAS 379 , 190 (2007), arXiv:astro-ph/0703126. [27] R. Mandelbaum, U. Seljak, and C. M. Hirata, JCAP 0808 , 006 (2008), 0805.2552. [28] A. F. Neto, L. Gao, P. Bett, S. Cole, J. F. Navarro, C. S. Frenk, S. D. M. White, V. Springel, and A. Jenkins, MNRAS 381 , 1450 (2007), 0706.2919. [29] G. Steigman and I. Tkachev, ApJ 522 , 793 (1999), astro- ph/9803008. 627 (2009), 0909.5203. 0.1 0.2 0.3 0.4 0.5$^{Α}$ 50 100 200 500 1000 2000 r$_{c}$ GLYPH<LBracket1> Mpc GLYPH<RBracket1>