We show that there are inflationary models for which perturbations in the energy momentum tensor , which are of second order in the scalar field , can not be neglected .
We first specify the conditions under which the usual first order perturbations are absent .
We then analyze classically , the growth and decay of our new type of perturbations for one mode of fluctuations \delta \phi _ { k } in the scalar field .
We generalize this analysis , considering the contribution from the whole spectrum of \delta \phi to a given wavelength of geometrical perturbations .
Finally , we discuss the evolution of the perturbations during the subsequent radiation dominated era and discuss the resulting spectrum of density fluctuations .
In the case of a massless scalar field we find a spectral index n = 4 .
For massive scalar fields we obtain n = 0 but the resulting amplitude of fluctuations for inflation around a GUT scale are by far too high .
Hence , ’ conventional ’ inflationary models must not be influenced by this new type of perturbations , in order to lead to acceptable perturbations .