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We will analyze two particular features of an exponential gravitationalLagrangian. On the one hand, while this choice of the Lagrangian density allowsfor two free parameters, only one scale, the cosmological constant, arises asfundamental when the proper Einsteinian limit is to be recovered. On the otherhand, 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 cosmologicalconstant can be recast.

Exponential Lagrangian for the Gravitational Field and the problem of Vacuum Energy