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No evidence for modifications of gravity from galaxy motions on cosmological scales

Nature Astronomy volume 2, pages 967–972 (2018)Cite this article

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Abstract

Current tests of general relativity (GR) remain confined to the scale of stellar systems or the strong gravity regime. A departure from GR on cosmological scales has been advocated1 as an alternative to the cosmological constant Λ (ref. 2) to account for the observed cosmic expansion history3,4. However, such models yield distinct values for the linear growth rate of density perturbations and consequently for the associated galaxy peculiar velocity field. Measurements of the resulting anisotropy of galaxy clustering5,6 have thus been proposed as a powerful probe of the validity of GR on cosmological scales7, but despite substantial efforts8,9, they suffer from systematic errors comparable to statistical uncertainties10. Here, we present the results of a forward-modelling approach that fully exploits the sensitivity of the galaxy velocity field to modifications of GR. We use state-of-the-art high-resolution N-body simulations of a standard GR (Λ cold dark matter (CDM)) model11 and a compelling f(R) model12—one of GR’s simplest variants, in which the Ricci scalar curvature, R, in the Einstein–Hilbert action is replaced by an arbitrary function of R—to build simulated catalogues of stellar-mass-selected galaxies through a robust match to the Sloan Digital Sky Survey13. We find that f(R) fails to reproduce the observed redshift-space clustering on scales of ~1–10 Mpc h−1, where h is the dimensionless Hubble parameter. Instead, the standard ΛCDM GR model agrees impressively well with the data. This result provides strong confirmation, on cosmological scales, of the robustness of Einstein’s general theory of relativity.

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Fig. 1: The small-scale galaxy clustering measured from the SDSS in redshift space, compared with a realization of the standard ΛCDM model.
Fig. 2: Multipoles of the redshift-space two-point correlation ξ(rσ, rπ).

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Koyama, K. Cosmological tests of modified gravity. Rep. Prog. Phys. 79, 046902–046945 (2016).

    Article  ADS  Google Scholar 

  2. Carroll, S. M. The cosmological constant. Living Rev. Rel. 4, 1 (2001).

    Article  MathSciNet  Google Scholar 

  3. Perlmutter, S. J. et al. Discovery of a supernova explosion at half the age of the Universe. Nature 391, 51–54 (1998).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Kaiser, N. Clustering in real space and in redshift space. Mon. Not. R. Astron. Soc. 227, 1–21 (1987).

    Article  ADS  Google Scholar 

  6. Peacock, J. A. et al. A measurement of the cosmological mass density from clustering in the 2dF Galaxy Redshift Survey. Nature 410, 169–173 (2001).

    Article  ADS  Google Scholar 

  7. Guzzo, L. et al. A test of the nature of cosmic acceleration using galaxy redshift distortions. Nature 451, 541–545 (2008).

    Article  ADS  Google Scholar 

  8. Scoccimarro, R. Redshift-space distortions, pairwise velocities and nonlinearities. Phys. Rev. D 70, 083007–083025 (2004).

    Article  ADS  Google Scholar 

  9. Taruya, A., Nishimichi, T. & Saito, S. Baryon acoustic oscillations in 2D: modeling redshift-space power spectrum from perturbation theory. Phys. Rev. D 82, 063522–063539 (2010).

    Article  ADS  Google Scholar 

  10. de la Torre, S. & Guzzo, L. Modelling non-linear redshift-space distortions in the galaxy clustering pattern: systematic errors on the growth rate parameter. Mon. Not. R. Astron. Soc. 427, 327–342 (2012).

    Article  ADS  Google Scholar 

  11. Klypin, A., Yepes, G., Gottlober, S., Prada, F. & Hess, S. MultiDark simulations: the story of dark matter halo concentrations and density profiles. Mon. Not. R. Astron. Soc. 457, 4340–4359 (2016).

    Article  ADS  Google Scholar 

  12. Felice, A. D. & Tsujikawa, S. f(R) theories. Living Rev. Rel. 13, 3 (2010).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Abbott, B. P. et al. GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119, 161101–161118 (2017).

    Article  ADS  Google Scholar 

  15. Goldstein, A. et al. An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817A. Astrophys. J. Lett. 848, L14 (2017).

    Article  ADS  Google Scholar 

  16. Khoury, J. & Weltman, A. Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93, 171104–171107 (2004).

    Article  ADS  Google Scholar 

  17. de la Torre, S. et al. The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at 0.5 < z < 1.2. Astron. Astrophys. 608, A44 (2017).

    Article  Google Scholar 

  18. Blake, C. et al. The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9. Mon. Not. R. Astron. Soc. 415, 2876–2891 (2011).

    Article  ADS  Google Scholar 

  19. Alam, S. et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. Mon. Not. R. Astron. Soc. 470, 2617–2652 (2017).

    Article  ADS  Google Scholar 

  20. Vale, A. & Ostriker, J. P. Linking halo mass to galaxy luminosity. Mon. Not. R. Astron. Soc. 353, 189–200 (2004).

    Article  ADS  Google Scholar 

  21. Schaye, J. et al. The EAGLE project: simulating the evolution and assembly of galaxies and their environments. Mon. Not. R. Astron. Soc. 446, 521–554 (2015).

    Article  ADS  Google Scholar 

  22. Blanton, M. R. et al. NYU-VAGC: a galaxy catalog based on new public surveys. Astron. J. 129, 2562–2578 (2005).

    Article  ADS  Google Scholar 

  23. Bruzual, G. & Charlot, S. Stellar population synthesis at the resolution of 2003. Mon. Not. R. Astron. Soc. 344, 1000–1028 (2003).

    Article  ADS  Google Scholar 

  24. Conroy, C. Modeling the panchromatic spectral energy distributions of galaxies. Ann. Rev. Astron. Astrophys. 51, 393–455 (2013).

    Article  ADS  Google Scholar 

  25. Ade, P. A. R. et al. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016).

    Article  Google Scholar 

  26. Behroozi, P. S., Wechsler, R. H. & Wu, H.-Y. The ROCKSTAR phase-space temporal halo finder and the velocity offsets of cluster cores. Astrophys. J. 762, 109–128 (2013).

    Article  ADS  Google Scholar 

  27. Monster, B. P. et al. Constraints on the relationship between stellar mass and halo mass at low and high redshift. Astrophys. J. 710, 903–923 (2010).

    Article  ADS  Google Scholar 

  28. McCullagh, N. et al. Revisiting HOD model assumptions: the impact of AGN feedback and assembly bias. Preprint at https://arxiv.org/abs/1705.01988 (2017).

  29. Shi, D., Li, B., Han, J., Gao, L. & Hellwing, W. A. Exploring the liminality: properties of halos and subhalos in borderline f(R) gravity. Mon. Not. R. Astron. Soc. 452, 3179–3191 (2015).

    Article  ADS  Google Scholar 

  30. He, J.-H., Hawken, A. J., Li, B. & Guzzo, L. Effective dark matter halo catalogue in f(R) gravity. Phys. Rev. Lett. 115, 071306–071310 (2015).

    Article  ADS  Google Scholar 

  31. Hu, W. & Sawicki, I. Models of f(R) cosmic acceleration that evade Solar System tests. Phys. Rev. D 76, 064004–064016 (2007).

    Article  ADS  Google Scholar 

  32. Schmidt, F., Vikhlinin, A. & Hu, W. Cluster constraints on f(R) gravity. Phys. Rev. D 80, 083505–083513 (2009).

    Article  ADS  Google Scholar 

  33. Fontanot, F., Puchwein, E., Springel, V. & Bianchi, D. Semi-analytic galaxy formation in f(R)-gravity cosmologies. Mon. Not. R. Astron. Soc. 436, 2672–2679 (2013).

    Article  ADS  Google Scholar 

  34. van den Bosch, F. C. et al. The importance of satellite quenching for the build-up of the red sequence of present-day galaxies. Mon. Not. R. Astron. Soc. 387, 79–91 (2008).

    Article  ADS  Google Scholar 

  35. Chabrier, G. Galactic stellar and substellar initial mass function. Publ. Astron. Soc. Pac. 115, 763–796 (2003).

    Article  ADS  Google Scholar 

  36. Kroupa, P. On the variation of the initial mass function. Mon. Not. R. Astron. Soc. 322, 231–246 (2001).

    Article  ADS  Google Scholar 

  37. Guo, Q., White, S. D. M., Li, C. & Boylan-Kolchin, M. How do galaxies populate dark matter halos? Mon. Not. R. Astron. Soc. 404, 1111–1120 (2010).

    ADS  Google Scholar 

  38. Li, C. & White, S. D. M. The distribution of stellar mass in the low-redshift Universe. Mon. Not. R. Astron. Soc. 398, 2177–2187 (2009).

    Article  ADS  Google Scholar 

  39. Blanton, M. R. & Roweis, S. K-corrections and filter transformations in the ultraviolet, optical, and near-infrared. Astron. J. 133, 734–754 (2007).

    Article  ADS  Google Scholar 

  40. Yang, X. et al. Galaxy groups in the SDSS DR4: I. The catalogue and basic properties. Astrophys. J. 671, 153–170 (2007).

    Article  ADS  Google Scholar 

  41. Davis, M. & Peebles, P. J. E. A survey of galaxy redshifts. V. The two-point position and velocity correlations. Astrophys. J. 267, 465–482 (1983).

    Article  ADS  Google Scholar 

  42. Landy, S. D. & Szalay, A. S. Bias and variance of angular correlation functions. Astron. J. 412, 64–71 (1993).

    Article  ADS  Google Scholar 

  43. Reid, B. A., Seo, H.-J., Leauthaud, A., Tinker, J. L. & White, M. A 2.5% measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies. Mon. Not. R. Astron. Soc. 444, 476–502 (2014).

    Article  ADS  Google Scholar 

  44. Kravtsov, A. V. et al. The dark side of the halo occupation distribution. Astrophys. J. 609, 35–49 (2004).

    Article  ADS  Google Scholar 

  45. Conroy, C., Wechsler, R. H. & Kravtsov, A. V. Modeling luminosity-dependent galaxy clustering through cosmic time. Astrophys. J. 647, 201–214 (2006).

    Article  ADS  Google Scholar 

  46. Reddick, R. M., Wechsler, R. H., Tinker, J. L. & Behroozi, P. The connection between galaxies and dark matter structures in the local Universe. Astrophys. J. 771, 30–61 (2013).

    Article  ADS  Google Scholar 

  47. Chaves-Montero, J. et al. Subhalo abundance matching and assembly bias in the EAGLE simulation. Mon. Not. R. Astron. Soc. 460, 3100–3118 (2016).

    Article  ADS  Google Scholar 

  48. Springel, V. The cosmological simulation code GADGET-2. Mon. Not. R. Astron. Soc. 364, 1105–1134 (2005).

    Article  ADS  Google Scholar 

  49. Teyssier, R. Cosmology hydrodynamics with adaptive mesh refinement. A new high-resolution code called RAMSES. Astron. Astrophys. 385, 337–364 (2002).

    Article  ADS  Google Scholar 

  50. Knollmann, S. R. & Knebe, A. AHF: AMIGA’s Halo Finder. Astrophys. J. Suppl. 182, 608–624 (2009).

    Article  ADS  Google Scholar 

  51. He, J.-H., Li, B. & Baugh, C. M. Subhalo abundance matching in f(R) gravity. Phys. Rev. Lett. 117, 221101–221105 (2016).

    Article  ADS  Google Scholar 

  52. Smee, S. A. et al. The multi-object, fiber-fed spectrographs for the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. Astron. J. 146, 40–71 (2013).

    Article  ADS  Google Scholar 

  53. Hawkins, E. et al. The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe. Mon. Not. R. Astron. Soc. 346, 78–96 (2003).

    Article  ADS  Google Scholar 

  54. Mohammad, F. G., de la Torre, S., Bianchi, D., Guzzo, L. & Peacock, J. A. Group–galaxy correlations in redshift space as a probe of the growth of structure. Mon. Not. R. Astron. Soc. 458, 1948–1963 (2016).

    Article  ADS  Google Scholar 

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Acknowledgements

J.H. is supported by a Durham co-fund Junior Research Fellowship; J.H. and B.L. acknowledge support by the European Research Council (ERC-StG-716532-PUNCA); L.G. acknowledges support by the European Research Council (ERC-AdG-291521-Darklight) and by the Italian Space Agency (ASI Grant I/023/12/0); B.L. and C.M.B. are also supported by UK STFC Consolidated Grants ST/P000541/1 and ST/L00075X/1.

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Authors and Affiliations

  1. Institute for Computational Cosmology, Department of Physics, Durham University, Durham, UK

    Jian-hua He, Baojiu Li & Carlton M. Baugh

  2. Dipartimento di Fisica, Universita’ degli Studi di Milano, Milan, Italy

    Luigi Guzzo

  3. INAF – Osservatorio Astronomico di Brera, Milan, Italy

    Luigi Guzzo

  4. INFN – Sezione di Milano, Milan, Italy

    Luigi Guzzo

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  1. Jian-hua He
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Contributions

All authors contributed to the development and writing of this paper. J.H. led the data analysis. B.L. conducted and provided the simulations. L.G. led the writing of the paper. C.M.B. and J.H. conceived the idea of data analysis.

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Correspondence to Jian-hua He.

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He, Jh., Guzzo, L., Li, B. et al. No evidence for modifications of gravity from galaxy motions on cosmological scales. Nat Astron 2, 967–972 (2018). https://doi.org/10.1038/s41550-018-0573-2

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