GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49>GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s57> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s56> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s55> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s54> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s52> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s51> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s54> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s56> GLYPH<s49>GLYPH<s46>GLYPH<s48>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s110> GLYPH<s115> GLYPH<s32> GLYPH<s115> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s48> GLYPH<s32> GLYPH<s115> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s48>GLYPH<s50> GLYPH<s32> GLYPH<s115> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s48>GLYPH<s53> GLYPH<s32> GLYPH<s115> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s49>GLYPH<s32> GLYPH<s32> GLYPH<s115> GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s48>GLYPH<s46>GLYPH<s48>GLYPH<s50> FIG. 4: Spectral index for F -term hybrid inflation with minimal kinetic terms (top green curve) and non-renormalizable corrections to the K¨ ahler. Figure is taken from [82]. Another symmetry - the Heisenberg symmetry - has also been invoked to protect the form of the K¨ ahler potential, see for a recent discussion in [635], generating a model where the effective K¨ ahler is a no-scale potential, that is of the form K = ln(Φ$_{i}$). This obviously solves the η -problem by canceling the exponential term exp( K ) $^{64}$. 64 There is a word of caution here, it is assumed that one can take the inflaton VEV above the Planck scale, as in the case of Heisenberg symmetry of the K¨ ahler potential, in order to realize chaotic type models [613, 634, 636]. However, this assumes that the K¨ ahler potential does not obtain any quantum corrections. Further note that non-renormalization theorem can only protect the superpotential terms [637], but the K¨ ahler potential generically obtains quantum corrections, which have been computed explicitly in some cases [638–640]. In string motivated models it is hard to realize chaotic type models of inflation with VEVs larger than the 4 d Planck scale. The presence of non-renormalizable correction to the kinetic terms has important conse- quences on the CMB predictions of the F -term hybrid model. In particular it can be used to realize a better agreement with the WMAP 5 measurement on the spectral index [72, 82]. It has been shown that the presence of the κ$_{s}$ term in Eq. (230) allow the model to; 1) lower the value of M responsible for the normalization of the spectrum for a given κ and 105