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In a recent paper in Astronomy & Astrophysics, Alimi & Koskas (2024) have highlighted in wCDM models derived from general relativity (with Dark Energy Universe numerical simulation data), a cosmological invariance of the distribution of dark matter (DM) halo shapes when expressed in terms of the non-linear fluctuations of the cosmic matter field. We show in this paper that this invariance persists when tested on numerical simulations performed with a different code, i. e. a different N-body solver, DUSTGRAIN-pathfinder simulation (Giocoli et al. 2018) and that it is also robust to the addition of neutrinos to the cold component of dark matter. However, this discovery raises crucial questions about the validity of this invariance in modified gravity models. Thus, we examine whether the invariance observed by Alimi & Koskas (2024) remains robust in the case of Hu & Sawicki models of modified gravity using numerical simulations performed by Giocoli et al. (2018). By comparing the results of advanced numerical simulations in these different theoretical frameworks, we found significant deviations from the invariance observed in the framework of wCDM models of GR. These deviations suggest that the nature of the gravitation significantly influences the shape of the DM halos. We then interpret this deviation observed in the modified gravity models from the GR models as due to the scalar-field screening effect corresponding to such f (R) -type theories. This one modifies the sphericalization process of DM halos during their formation, precisely because the critical mass at which this scalar field becomes non-negligible is the mass at which the deviation appears. To this extent, the deviation from cosmological invariance in the shape of DM halos is a cosmological probe of the nature of gravity, and the mass scale at which it appears can be used to estimate the fₑ₀ parameter of such theories.
Koskas et al. (Fri,) studied this question.