In this section we wish to consider quantum effects. In the work that we have done in the present chapter we have made an effort to write the scalar field as a function of R, i.e. and using we have written as an effective density for the scalar field. Thus inflation and quantum tunnelling require the same condition. Or in other words, inflation is simply a classical description of quantum tunnelling. We call this hypothesis Quantum Inflation .
Quantum inflation is easy to validate for ordinary densities, either or , that behave like .
With our discussion of the scalar field we have written so it would seem that the idea of quantum inflation also works for scalar fields. In terms of scalar fields then this quantization procedure is different to what other people do with quantization. Let us now study this procedure. We can see that the above method of quantizing the scalar field directly is still consistent with our idea of Quantum Inflation. Thus if then also in the same way.