content_image/372941.jpg content_image/372938.jpg content_image/372937.jpg
small superpotential coupling in agreement with a low weight of cosmic strings, the inflaton VEV already shoots up above the Planck scale for 60 e-foldings. 

The minimal version of D -term inflation does not predict a detectable amount of non- Gaussianity, as only one field effectively rolls and fluctuates during inflation, at least. The reason is that in the inflationary valley, the waterfall fields coupled to the inflaton have mass of the order of the GUT scale, m 2 B ≃ λ $^{2}$S$^{2}$± g 2 $_{ξ}$ξ , much heavier than the Hubble scale during inflation. But in case of the presence of a light (super)field S$_{2}$ with mass µ$_{2}$ in the theory, both S and S$_{2}$ contribute to the primordial fluctuations, and can create a large amount of non-Gaussianities, well above the level of one field inflation [657]. Furthermore, this will also induce large isocurvature perturbations which would modify the spectral tilt and the primordial spectrum $^{68}$. 

## 3. D -term inflation from superconformal field theory 

The standard picture described in the previous section has been modified in [462] to take into account of the possibility that SUGRA is constructed from a superconformal field theory (see [658] for a review). In this framework the theory is described by a conformal K¨ ahler N and a conformal superpotential W . In this formulation, which allows to embed any SUGRA of N ≤ 4, the field content are some chiral superfield Φ$_{i}$ and a field Y , called the “conformon”, whose modulus fixes the Planck scale: 

<img src='content_image/372941.jpg'>

where K is the SUGRA K¨ ahler potential, related to the conformal K¨ ahler by 

The theory is fully described once a conformal superpotential W is chosen, related to the SUGRA superpotential, W , by 

<img src='content_image/372938.jpg'>

<img src='content_image/372937.jpg'>

