This inflation is then called semi-shifted, since only the VEVs of Ψ , ¯ Ψ are shifted away from 0. As a consequence the breaking during inflation is G$_{P}$$_{S}$ → SU (3)$_{c}$ × SU (2)$_{L}$ × U (1)$_{R}$ × U $^{(1)$_{B}$}$− L leaving the second symmetry breaking SU (3)$_{c}$ × SU (2)$_{L}$ × U (1)$_{R}$ × U $^{(1)$_{B}$}$− L → G$_{S}$$_{M}$ for the end of inflation. As a consequence, the model predicts the formation of B-L cosmic strings, which can have important phenomenological consequences [644], including on the CMB predictions of the model. When taking into account of the SUGRA corrections, the spectral index [84] is found in the range n$_{s}$ ∈ [0 . 98 , 1 . 05] for m ∈ [0 . 5 , 2 . 5] × 10 15 GeV, in agreement with WMAP data in presence of cosmic strings. The running and the ratio of tensor to scalar is again found well below expected detection limits. It was first noticed in Ref. [627] that inflation with a perfectly flat inflaton potentials in SUSY/SUGRA can be constructed using a constant contribution to the D -term, and a rather complicated superpotential used to drive the field dependent contributions to the D - terms to 0. In [645, 646], a very simple superpotential was proposed to achieve the similar result, where it was noticed that the radiative correction would lift this flat direction and drive inflation. In addition, it was noticed that the η problem arising in F -term models does not appear for D -terms driven inflation even for the non-minimal K¨ ahler potential because the D - sector of the potential does not receive exponential contributions from non-minimal SUGRA. The model requires the presence of a Fayet-Iliopoulos (FI) term ξ , and therefore a U (1)$_{ξ}$ symmetry that allows or generates it. This model rapidly became one of the most studied models of inflation because of its stability in SUGRA, and its stability when embedded in other high energy frameworks such as SUSY GUTs (see for example [64, 66]), and SUGRA from superconformal field theory [462]. The model was also found to be a good low-energy description of brane inflation [647, 648]) proposed in the context of extra-dimensional cosmology. F. Inflation from D -terms in SUSY and SUGRA M 2 − m $^{2}$/ 2 κ 2 > 0 〈 Φ 〉 = 〈 ¯ Φ 〉 = 0 , 〈 Ψ 〉 = ± ˜ M , 〈 ¯ Ψ 〉 = − 2 κ 〈 Ψ 〉 m S , 〈 S 〉 > 0 . (245) 114