NEW CONTRIBUTION TO COSMOLOGICAL PERTURBATIONS OF SOME INFLATIONARY MODELS

We show that there are inflationary models for which perturbations in the energy-momentum tenser, which are of second order in the scalar fi eld, cannot be neglected. We first specify the conditions under which the usual first order perturbations are absent. We then analyze classi cally the growth and decay of our new type of perturbations for one mo de of fluctuations delta phi(k) in the scalar field. We generalize thi s analysis, considering the contribution from the whole spectrum of de lta phi to a given wavelength of geometrical perturbations. Finally, w e discuss the evolution of the perturbations during the subsequent rad iation-dominated era and discuss the resulting spectrum of ,density fl uctuations. 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 resulti ng amplitude of fluctuations for inflation around a GUT scale are by f ar too high. Hence, ''conventional'' inflationary models must not be i nfluenced by this new type of perturbations, in order to lead to accep table perturbations.