Exponential Lagrangian for the Gravitational Field and the problem of   Vacuum Energy
  We will analyze two particular features of an exponential gravitational Lagrangian. On the one hand, while this choice of the Lagrangian density allows for two free parameters, only one scale, the cosmological constant, arises as fundamental when the proper Einsteinian limit is to be recovered. On the other hand, the vacuum energy arising from $f(R)$ theories such that $f(0)\neq 0$ needs a cancellation mechanism, by which the present value of the cosmological constant can be recast. 
O.M. Lecian, G. Montani