  We show that it is possible to obtain inflation and also solve the
cosmological constant problem. The theory is invariant under changes of the
Lagrangian density $L$ to $L+const$. Then the constant part of a scalar field
potential $V$ cannot be responsible for inflation. However, we show 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 equations with an effective
scalar field potential $V_{eff}$ which has generally 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.
