Alejandro Hernandez-Arboleda

arXiv2023

Palatini $f(R)$ gravity tests in the weak field limit: Solar System, seismology and galaxies

Palatini $f(R)$ gravity is probably the simplest extension of general relativity (GR) and the simplest realization of a metric-affine theory. It has the same number of degrees of freedom as GR and, in vacuum, it is straightforwardly mapped into GR with a cosmological constant. The mapping between GR and Palatini $f(R)$ inside matter is possible but at the expense of reinterpreting the meaning of the matter fields. The physical meaning and consequences of such mapping will depend on the physical context. Here we consider three such cases within the weak field limit: Solar System dynamics, planetary internal dynamics (seismology), and galaxies. After revising our previous results on the Solar System and Earth's seismology, we consider here the possibility of $f(R)$ Palatini as a dark matter candidate. For any $f(R)$ that admits a polynomial approximation in the weak field limit, we show here, using SPARC data and a recent method that we proposed, that the theory cannot be used to replace dark matter in galaxies. We also show that the same result applies to the Eddington-inspired Born-Infeld gravity. Differently from the metric $f(R)$ case, the rotation curve data are sufficient for this conclusion. This result does not exclude a combination of modified gravity and dark matter.

gr-qc↗

arXiv2023

Normalized additional velocity distribution: testing the radial profile of dark matter halos and MOND

We propose a complementary and fast approach to study galaxy rotation curves directly from the sample data, instead of individual fits. With this approach, some relevant tests can be done analytically. It is based on a dimensionless difference between the observational rotation curve and the expected one from the baryonic matter ($δV^2$) as a function of the normalized radius $r_n$ (i.e., for all galaxies, $0 < r_n < 1$). Using 153 galaxies from the SPARC galaxy sample, we find the observational distribution of $δV^2$. Considering radii with $0.2 < r_n < 0.9$, most of the SPARC data are close to the curve $δV^2 = r_n^{0.42}$, and about $95\%$ of the SPARC data is between the curves $δV^2 = r_n^{2.2}$ and $δV^2 = 2 r_n^{0.38} - r_n^{1.9} $. We consider three well known dark matter halo models (NFW, Burkert and DC14), a simple dark matter rotation curve profile for the purpose of model comparison (Arctan$_α$) and one modified gravity model without dark matter (MOND). By comparing the observational data distribution with the model-inferred data, we confirm that the NFW halo lacks the necessary diversity to reproduce several observed rotation curves, while Burkert and DC14 models have better concordance with observational data. The lowest $δV^2$ curves that can be found from NFW are linear on the normalized radius (i.e., $δV^2_{NFW} = r_n$), while for Burkert $δV^2_{Bur} = r_n^2$ (this result is independent of the halo density parameter, i.e., $ρ_{c}$ or $ρ_{s}$). MOND only covers the very central region of the observed distribution, hence it also lacks the necessary diversity, which in turn is related to larger $χ^2$ values. In a second paper, the method will be extended to consider other classes of modified gravity models.

astro-ph.GA↗