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 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] which affects the relation M ( κ ) at large κ , and imposes new stringent bounds on M < ∼ 2 × 10 15 GeV, and [484, 486] 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 61 Small values of κ can render the scale of inflation very low, as low as the TeV scale [618–621]. 102 N$_{Q}$ = 32 π 3 κ $^{2}$N M 2 M 2 P ∫ z$_{Q}$ 1 d z zf ( z ) , with f ( z ) = ( z + 1) ln(1 + $_{z}$− $^{1}$) + ( z − 1) ln(1 − $_{z}$− $^{1}$) . (224) ( δT T ) 2 COBE = ( δT T ) 2 Infl + ( δT T ) 2 CS , (225) κ < ∼ 7 × $_{10}$− $_{7}$126 N$_{Q}$ , (226)