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) $^{34}$. 

## 2. Inflaton-induced SUGRA corrections 

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 

