Realistic simulations of galaxy formation in f(R) modified gravity


Future astronomical surveys will gather information that will allow gravity to be tested on cosmological scales, where general relativity is currently poorly constrained. We present a set of cosmological hydrodynamical simulations that follow galaxy formation in f(R) modified gravity models and are dedicated to finding observational signatures to help distinguish general relativity from alternatives using this information. The simulations employ the IllustrisTNG model and a new modified gravity solver in AREPO, allowing the interplay of baryonic feedback and modified gravity to be studied in the same simulation, and the degeneracy between them in the matter power spectrum to be resolved. We find that the neutral hydrogen power spectrum is suppressed substantially in f(R) gravity, which allows this model to be constrained using upcoming data from the Square Kilometre Array. Disk galaxies can form in our f(R) gravity simulations, even in the partially screened regime, and their galaxy stellar properties are only mildly affected. We conclude that modified gravity allows the formation of realistic galaxies and leaves observable signatures on large scales.

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Fig. 1: Edge- and face-on views of four different, randomly selected disk galaxies from our simulations.
Fig. 2: The relative effects of modified gravity and baryonic feedback on the total matter power spectrum.
Fig. 3: The three-dimensional matter power spectrum of the different matter components.
Fig. 4: The stellar and gaseous properties of galaxies.

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.

Code availability

The simulation code AREPO21 is currently not publicly available. The analysis scripts used to analyse the simulation output can be made available to the reader on request.


  1. 1.

    Buchdahl, H. A. Non-linear Lagrangians and cosmological theory. Mon. Not. R. Astron. Soc. 150, 1–8 (1970).

    ADS  Article  Google Scholar 

  2. 2.

    Lombriser, L. & Taylor, A. Breaking a dark degeneracy with gravitational waves. J. Cosmol. Astropart. Phys. 2016, 031 (2016).

    Article  Google Scholar 

  3. 3.

    Sakstein, J. & Jain, B. Implications of the neutron star merger GW170817 for cosmological scalar-tensor theories. Phys. Rev. Lett. 119, 251303 (2017).

    ADS  Article  Google Scholar 

  4. 4.

    Ezquiaga, J. M. & Zumalacárregui, M. Dark energy after GW170817: dead ends and the road ahead. Phys. Rev. Lett. 119, 251304 (2017).

    ADS  Article  Google Scholar 

  5. 5.

    Lombriser, L. & Lima, N. A. Challenges to self-acceleration in modified gravity from gravitational waves and large-scale structure. Phys. Lett. B 765, 382–385 (2017).

    ADS  MATH  Article  Google Scholar 

  6. 6.

    Khoury, J. & Weltman, A. Chameleon cosmology. Phys. Rev. D 69, 044026 (2004).

    ADS  MathSciNet  Article  Google Scholar 

  7. 7.

    Will, C. M. The confrontation between general relativity and experiment. Living Rev. Relativ. 17, 4 (2014).

    ADS  MATH  Article  Google Scholar 

  8. 8.

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

    ADS  Article  Google Scholar 

  9. 9.

    Sotiriou, T. P. & Faraoni, V. f(R) theories of gravity. Rev. Mod. Phys. 82, 451–497 (2010).

    ADS  MATH  Article  Google Scholar 

  10. 10.

    Schmidt, F. Dynamical masses in modified gravity. Phys. Rev. D 81, 103002 (2010).

    ADS  Article  Google Scholar 

  11. 11.

    Zhao, G.-B., Li, B. & Koyama, K. Testing gravity using the environmental dependence of dark matter halos. Phys. Rev. Lett. 107, 071303 (2011).

    ADS  Article  Google Scholar 

  12. 12.

    Lombriser, L., Li, B., Koyama, K. & Zhao, G.-B. Modeling halo mass functions in chameleon f(R) gravity. Phys. Rev. D 87, 123511 (2013).

    ADS  Article  Google Scholar 

  13. 13.

    Puchwein, E., Baldi, M. & Springel, V. Modified-gravity-GADGET: a new code for cosmological hydrodynamical simulations of modified gravity models. Mon. Not. R. Astron. Soc. 436, 348–360 (2013).

    ADS  Article  Google Scholar 

  14. 14.

    Hellwing, W. A., Li, B., Frenk, C. S. & Cole, S. Hierarchical clustering in chameleon f(R) gravity. Mon. Not. R. Astron. Soc. 435, 2806–2821 (2013).

    ADS  Article  Google Scholar 

  15. 15.

    Zivick, P., Sutter, P. M., Wandelt, B. D., Li, B. & Lam, T. Y. Using cosmic voids to distinguish f(R) gravity in future galaxy surveys. Mon. Not. R. Astron. Soc. 451, 4215–4222 (2015).

    ADS  Article  Google Scholar 

  16. 16.

    Mitchell, M. A., He, J.-h, Arnold, C. & Li, B. A general framework to test gravity using galaxy clusters—I. Modelling the dynamical mass of haloes in f(R) gravity. Mon. Not. R. Astron. Soc. 477, 1133–1152 (2018).

    ADS  Article  Google Scholar 

  17. 17.

    Li, B. & Shirasaki, M. Galaxy–galaxy weak gravitational lensing in f(R) gravity. Mon. Not. R. Astron. Soc. 474, 3599–3614 (2018).

    ADS  Article  Google Scholar 

  18. 18.

    Arnold, C., Puchwein, E. & Springel, V. The Lyman α forest in f(R) modified gravity. Mon. Not. R. Astron. Soc. 448, 2275–2283 (2015).

    ADS  Article  Google Scholar 

  19. 19.

    Hammami, A., Llinares, C., Mota, D. F. & Winther, H. A. Hydrodynamic effects in the symmetron and f(R)-gravity models. Mon. Not. R. Astron. Soc. 449, 3635–3644 (2015).

    ADS  Article  Google Scholar 

  20. 20.

    He, J.-h & Li, B. Accurate method of modeling cluster scaling relations in modified gravity. Phys. Rev. D 93, 123512 (2016).

    ADS  Article  Google Scholar 

  21. 21.

    Springel, V. E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh. Mon. Not. R. Astron. Soc. 401, 791–851 (2010).

    ADS  Article  Google Scholar 

  22. 22.

    Pillepich, A. et al. First results from the IllustrisTNG simulations: the stellar mass content of groups and clusters of galaxies. Mon. Not. R. Astron. Soc. 475, 648–675 (2018).

    ADS  Article  Google Scholar 

  23. 23.

    Springel, V. et al. First results from the IllustrisTNG simulations: matter and galaxy clustering. Mon. Not. R. Astron. Soc. 475, 676–698 (2018).

    ADS  Article  Google Scholar 

  24. 24.

    Genel, S. et al. The size evolution of star-forming and quenched galaxies in the IllustrisTNG simulation. Mon. Not. R. Astron. Soc. 474, 3976–3996 (2018).

    ADS  Article  Google Scholar 

  25. 25.

    Marinacci, F. et al. First results from the IllustrisTNG simulations: radio haloes and magnetic fields. Mon. Not. R. Astron. Soc. 480, 5113–5139 (2018).

    ADS  Google Scholar 

  26. 26.

    Nelson, D. et al. First results from the IllustrisTNG simulations: the galaxy colour bimodality. Mon. Not. R. Astron. Soc. 475, 624–647 (2018).

    ADS  Article  Google Scholar 

  27. 27.

    Terukina, A. et al. Testing chameleon gravity with the Coma cluster. J. Cosmol. Astropart. Phys. 4, 013 (2014).

    ADS  Article  Google Scholar 

  28. 28.

    Arnold, C., Fosalba, P., Springel, V., Puchwein, E. & Blot, L. The modified gravity lightcone simulation project I: statistics of matter and halo distributions. Mon. Not. R. Astron. Soc. 483, 790–805 (2019).

    ADS  Article  Google Scholar 

  29. 29.

    Hellwing, W. A. et al. The effect of baryons on redshift space distortions and cosmic density and velocity fields in the EAGLE simulation. Mon. Not. R. Astron. Soc. 461, L11–L15 (2016).

    ADS  Article  Google Scholar 

  30. 30.

    Laureijs, R. et al. Euclid definition study report. Preprint at (2011).

  31. 31.

    Weinberger, R. et al. Simulating galaxy formation with black hole driven thermal and kinetic feedback. Mon. Not. R. Astron. Soc. 465, 3291–3308 (2017).

    ADS  Article  Google Scholar 

  32. 32.

    Winther, H. A. et al. Modified gravity N-body code comparison project. Mon. Not. R. Astron. Soc. 454, 4208–4234 (2015).

    ADS  Article  Google Scholar 

  33. 33.

    Villaescusa-Navarro, F. et al. Ingredients for 21 cm intensity mapping. Astrophys. J. 866, 135 (2018).

    ADS  Article  Google Scholar 

  34. 34.

    Santos, M. et al. Cosmology from a SKA H i intensity mapping survey. In Proc. Advancing Astrophysics with the Square Kilometre Array (AASKA14) 19 (2015).

  35. 35.

    Pillepich, A. et al. Simulating galaxy formation with the IllustrisTNG model. Mon. Not. R. Astron. Soc. 473, 4077–4106 (2018).

    ADS  Article  Google Scholar 

  36. 36.

    Altay, G., Theuns, T., Schaye, J., Booth, C. M. & Dalla Vecchia, C. The impact of different physical processes on the statistics of Lyman-limit and damped Lyman α absorbers. Mon. Not. R. Astron. Soc. 436, 2689–2707 (2013).

    ADS  Article  Google Scholar 

  37. 37.

    Behroozi, P. S., Wechsler, R. H. & Conroy, C. The average star formation histories of galaxies in dark matter halos from z = 0–8. Astrophys. J. 770, 57 (2013).

    ADS  Article  Google Scholar 

  38. 38.

    Giodini, S. et al. Stellar and total baryon mass fractions in groups and clusters since redshift 1. Astrophys. J. 703, 982–993 (2009).

    ADS  Article  Google Scholar 

  39. 39.

    Lovisari, L., Reiprich, T. H. & Schellenberger, G. Scaling properties of a complete X-ray selected galaxy group sample. Astron. Astrophys. 573, A118 (2015).

    ADS  Article  Google Scholar 

  40. 40.

    Planck Collaboration et al. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016).

    Article  Google Scholar 

  41. 41.

    Vogelsberger, M. et al. Properties of galaxies reproduced by a hydrodynamic simulation. Nature 509, 177–182 (2014).

    ADS  Article  Google Scholar 

  42. 42.

    Vogelsberger, M. et al. Introducing the illustris project: simulating the coevolution of dark and visible matter in the Universe. Mon. Not. R. Astron. Soc. 444, 1518–1547 (2014).

    ADS  Article  Google Scholar 

  43. 43.

    Sawicki, I. & Bellini, E. Limits of quasistatic approximation in modified-gravity cosmologies. Phys. Rev. D. 92, 084061 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  44. 44.

    He, J.-h, Guzzo, L., Li, B. & Baugh, C. M. No evidence for modifications of gravity from galaxy motions on cosmological scales. Nat. Astron. 2, 967–972 (2018).

    ADS  Article  Google Scholar 

  45. 45.

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

    ADS  Article  Google Scholar 

  46. 46.

    Li, B., Zhao, G.-B., Teyssier, R. & Koyama, K. ECOSMOG: an efficient code for simulating modified gravity. J. Cosmol. Astropart. Phys. 1, 51 (2012).

    ADS  Article  Google Scholar 

  47. 47.

    Bose, S. et al. Speeding up N-body simulations of modified gravity: chameleon screening models. J. Cosmol. Astropart. Phys. 2017, 050 (2017).

    MathSciNet  Article  Google Scholar 

  48. 48.

    Llinares, C., Mota, D. F. & Winther, H. A. ISIS: a new N-body cosmological code with scalar fields based on RAMSES. Code presentation and application to the shapes of clusters. Astron. Astrophys. 562, A78 (2014).

    ADS  Article  Google Scholar 

  49. 49.

    Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. (eds) Numerical Recipes 3rd edn (Cambridge Univ. Press, 2007).

  50. 50.

    Arnold, C., Springel, V. & Puchwein, E. Zoomed cosmological simulations of Milky Way-sized haloes in f(R) gravity. Mon. Not. R. Astron. Soc. 462, 1530–1541 (2016).

    ADS  Article  Google Scholar 

  51. 51.

    Ferrero, I. et al. Size matters: abundance matching, galaxy sizes, and the Tully–Fisher relation in EAGLE. Mon. Not. R. Astron. Soc. 464, 4736–4746 (2017).

    ADS  Article  Google Scholar 

  52. 52.

    Benitez-Llambay, A. Py-SPHviewer version 1.0.0, (2015).

  53. 53.

    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).

    ADS  Article  Google Scholar 

  54. 54.

    D’Souza, R., Vegetti, S. & Kauffmann, G. The massive end of the stellar mass function. Mon. Not. R. Astron. Soc. 454, 4027–4036 (2015).

    ADS  Article  Google Scholar 

  55. 55.

    Bernardi, M. et al. The massive end of the luminosity and stellar mass functions: dependence on the fit to the light profile. Mon. Not. R. Astron. Soc. 436, 697–704 (2013).

    ADS  Article  Google Scholar 

  56. 56.

    Baldry, I. K. et al. Galaxy and mass assembly (GAMA): the galaxy stellar mass function at z < 0.06. Mon. Not. R. Astron. Soc. 421, 621–634 (2012).

    ADS  Google Scholar 

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We thank the IllustrisTNG collaboration for allowing us to use their baryonic model to carry out the simulations presented in this work. We are grateful to V. Springel and R. Weinberger for their help with the AREPO code and for discussions on the results, and to A. Benitez-Llambay for making Py-SPHViewer52 available. Special thanks to C. Frenk and J. He for their comments on the results. The work described in this paper is supported by the European Research Council through an ERC Starting Grant (ERC-StG-716532-PUNCA). B.L. is additionally supported by STFC consolidated grants ST/P000541/1 and ST/L00075X/1. The cosmological simulations described in this work were run on the DiRAC Data Centric System at Durham University, UK, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure.

Author information




C.A. and B.L. planned the project. C.A. developed, implemented and optimized (together with B.L.) the modified gravity solver AREPO, ran the simulations and performed the main part of the analysis. M.L. performed the analysis for the H i power spectrum. C.A., B.L. and M.L. interpreted the results. C.A. wrote the manuscript with contributions from M.L. and B.L.

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Correspondence to Christian Arnold.

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Peer review information: Nature Astronomy thanks Simeon Bird, Bridget Falck and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Arnold, C., Leo, M. & Li, B. Realistic simulations of galaxy formation in f(R) modified gravity. Nat Astron 3, 945–954 (2019).

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