The gravity lagrangian according to solar system experiments

In this work we show that the gravity lagrangian f® 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 analysing a set of inequalities that any f® theory must satisfy in order to be compatible with laboratory and solar system observational constraints. This result implies that the recently suggested f® 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 speed-up.