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critical point, z = 1, which ends inflation. Thus, the quadrupole value for the inflaton, z$_{Q}$ ≡ S 2 $_{Q}$/M $^{2}$, is obtained by solving 

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The normalization to COBE allows to fix the scale M as a function of κ . If the breaking of G does not produce cosmic strings, the contribution to the quadrupole anisotropy sim- ply comes from the inflationary contribution (see Eq. (34)) and the observed value can be obtained even with a coupling κ close to unity [62] $^{61}$. However it has been shown that the formation of cosmic strings at the end of F -term inflation is highly probable when the model is embedded in SUSY GUTs [444]. In that case, the normalization to COBE receives two contributions [64, 483], one from inflation ( δT/T )$_{infl}$ ∝ V 3 / $^{2}$/V ′ , and the other from cosmic strings ( δT/T )$_{CS}$ ∝ Gµ , where µ is the mass per unit length of the strings (see Sec. III G). The relation between M and κ from the normalization of the power-spectrum is now obtained by solving [483] 

<img src='content_image/331566.jpg'>

which affects the relation M ( κ ) at large κ , and imposes new stringent bounds on M < ∼ 2 × 10 15 GeV, and [484, 486] 

<img src='content_image/331567.jpg'>

coming from imposing that the weight of cosmic strings in the WMAP3 data is less than < ∼ 10% [263]. This constraint can be made less stringent if some other sector of the Higgs potential imposes that some components of Φ , Φ acquire an ultra-large mass before inflation, during previous symmetry breaking [486]. 

Once M is fixed, the spectral index n$_{s}$ can also be computed as a function of the coupling constant. The range found is n$_{s}$ ∈ [0 . 98 , 1] whether cosmic strings form or not [486, 622], and by including the soft-SUSY breaking terms within minimal kinetic terms in the K¨ ahler potential, the spectral index can be brought down to 0 . 928 ≤ n$_{s}$ ≤ 1 . 008 [623]. This represents the most important difference with Linde’s original model, where a blue tilt is generated. Note however that when cosmic strings form, the coupling constant has to be 

