The Gravity Lagrangian According to Solar System Experiments

In this work we show that the gravity Lagrangian $f(R)$ at relatively low curvatures in both metric and Palatini formalisms is a bounded function that can only depart from the linearity within the limits defined by well-known functions. We obtain those functions by analyzing a set of inequalities that any $f(R)$ theory must satisfy in order to be compatible with laboratory and solar system observational constraints. This result implies that the recently suggested $f(R)$ gravity theories with nonlinear terms that dominate at low curvatures are incompatible with observations and, therefore, cannot represent a valid mechanism to justify the cosmic speedup.