F(R) Gravity - Observational Tests

Observational Tests

As there are many potential forms of f(R) gravity, it is difficult to find generic tests. Additionally, since deviations away from General Relativity can be made arbitrarily small in some cases, it is impossible to conclusively exclude some modifications. Some progress can be made, without assuming a concrete form for the function f(R) by Taylor expanding

The first term is like the cosmological constant and must be small. The next coefficient a₁ can be set to one as in general relativity. For metric f(R) gravity (as opposed to Palatini or metric-affine f(R) gravity), the quadratic term is best constrained by fifth force measurements, since it leads to a Yukawa correction to the gravitational potential. The best current bounds are |a₂| < 4 × 10−9m2 or equivalently |a₂| < 2.3 × 1022 GeV−2.

The parameterized post-Newtonian formalism is designed to be able to constrain generic modified theories of gravity. However, f(R) gravity shares many of the same values as General Relativity, and is therefore indistinguishable using these tests. In particular light deflection is unchanged, so f(R) gravity, like General Relativity, is entirely consistent with the bounds from Cassini tracking.