FROM INFLATION TO A ZERO COSMOLOGICAL CONSTANT PHASE WITHOUT FINE-TUNING

We show that it is possible to obtain inflation and also solve the cos mological constant problem. The theory is invariant under changes of t he Lagrangian density L to L+ const. Then the constant part of a scale r field potential V cannot be responsible for inflation. However, we s how that inflation can be driven by a condensate of a four index field strength. A constraint appears which correlates this condensate to V. After a conformal transformation, the equations are the standard GR e quations with an effective scalar field potential V-eff which has gene rally an absolute minimum V-eff=0 independently of V and without fine tuning. We also show that, after inflation, the usual reheating phase scenario (from oscillations around the absolute minimum) is possible.