The first term in Eq. (141), being field-independent, this term can affect the cosmological constant problem in SUGRA, but does not affect the discussion of the gauge hierarchy prob- lem. However, this term is always absent in SUSY theories, which possess equal numbers of bosonic and fermionic degrees of freedom. In Ref. [413, 414], it was shown that for unbroken N = 1 global SUSY, Str M n is identically vanishing for any n , due to the fermion-boson degeneracy within SUSY multiplets. It was argued that the term Str M 2 vanishes [414], as a field identity, if global SUSY is spontaneously broken in the absence of anomalous U (1) factors [413]. Anyway, the third term in Eq. (141), plays the most important role in inflationary models in lifting the flat potential for the inflaton. It was argued in [415], that in the derivation of [413], an explicit use has been made of the fact that all first order partial derivatives of the tree-level effective potential to the fields vanish. This limits the region of applicability of the simple Coleman-Weinberg formula in the context of inflationary models. Only at extremum (or saddle) points it is justified to throw away the second term of Eq. (141) $^{34}$. Since non-zero inflationary potential gives rise to SUSY breaking, the scale of which is given by the time dependent Hubble parameter. It is important to know how this will af- fect any other light scalar field during and after inflation, in particular the flat directions of MSSM. At early times this breaking is dominant over breaking from the hidden sec- tor $^{35}$. After the end of inflation, in most models the inflaton oscillates and its finite energy density still dominates and breaks SUSY in the visible sector. A particular class of non- renormalizable interaction terms induced by the inflaton arise if the K¨ ahler potential has a 2. Inflaton-induced SUGRA corrections 34 For a particular case of SUSY model of inflation, known as the hybrid inflation (see the discussion in section IVE.1, the Coleman-Weinberg formula given by the third term in Eq. (141) is applicable only in the global minimum and along the inflationary valley, because here all derivatives in the tree-level potential vanish. If one wishes to study the field dynamics throughout the phase space, one requires special care [415]. 35 Note that this does not replace the soft SUSY breaking terms required to solve the problems for the low energy physics, such as addressing the hierarchy problem or the electroweak symmetry breaking within MSSM, etc. 63