Palatini f(R) gravity tests in 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.

Automated summary

Palatini f(R) gravity is a simple extension of general relativity that can be mapped into GR with a cosmological constant. By reinterpreting the meaning of matter fields, GR and Palatini f(R) can be mapped within matter. In the weak field limit, we consider three cases and find that Palatini f(R) cannot replace dark matter in galaxies.