in Eq. (254). These works were partly motivated by the fact that the model was thought incompatible with the observations because the cosmic strings had been found responsible for most of the temperature anisotropies (75%), in contradiction with observations ( < ∼ 10%) [64]. Other motivations include the embedding of D -term inflation in strings theory, where FI term are generically present, but at a much lower scale than that imposed by the COBE normalization. They either assume that extra symmetry or extra fields are present to render the defects unstable, or add couplings in the superpotential to produce the strings before or during inflation or add couplings to allow for a normalization to COBE with lighter cosmic strings (then reducing their impact on the CMB). It is first possible to assume that the Higgs fields are charged not only under U (1)$_{ξ}$, $^{but also under some additional non-abelian local symmetry [462]. For example, if Φ}$− that takes a non-vanishing VEV, √$_{ξ}$$_{, is also a doublet under some other symmetry}$ SU (2)$_{a}$, the symmetry breaking at the end of inflation follows: SU (2)$_{a}$ × U (1)$_{ξ}$ → U $_{(1)}$′ , (260) and no topologically stable cosmic strings form (though embedded strings would form, like during the electro-weak symmetry breaking). Rendering the cosmic strings unstable by enlarging the symmetries of the theory can also be achieved by assuming two additional fields [462, 655]. For example, if a second pair of Higgs fields, ˜ $^{φ}$± , carry some charges identical to $^{φ}$± under U (1)$_{ξ}$. Thus the theory possesses an extra accidental global symmetry SU (2), since the potential (written here in global SUSY) is given by 69 V ( $^{φ}$±, ˜ $^{φ}$± ) = g 2 2 ( | φ$_{+}$ | 2 + | ˜ φ$_{+}$ | 2 − | $^{φ}$− | 2 − | ˜ $^{φ}$− | 2 − ξ ) 2 + λ $^{2}$S2 ( | φ$_{+}$ | 2 + | ˜ φ$_{+}$ | 2 + | $^{φ}$− | 2 + | ˜ $^{φ}$− | 2 ) + ∣ φ$_{+}$$^{φ}$− − ˜ φ$_{+}$ ˜ $^{φ}$− ∣ , (261) SU (2)$_{glob}$ × U (1)$_{ξ}$ → U (1)$_{glob}$ , (262) $^{φ}$− $^{φ}$− $^{φ}$− ∣$^{2}$ which is now invariant under the exchange φ$_{+}$ ↔ ˜ φ$_{+}$ and ˜ $^{φ}$− ↔ $^{φ}$− . When the Higgs fields settle in the global minimum, a global U(1) symmetry is left unbroken and the symmetry breaking at the end of inflation is of the form: 69 In [462], the same idea is proposed, though they employ only 1 extra Higgs fields φ ′ with a charge identical to $^{φ}$− . 121