content_image/349477.jpg content_image/349478.jpg
Unfortunately, in these models the value of f$_{NL}$ is very small and undetectable by the future experiments. The expression is also a generalization of [575], derived for the two field case. Similar exercise has been performed for models of multi-field inflation with non-canonical kinetic terms in [576, 577], we will discuss such models of inflation in Sec. VIII B. 

Non-Gaussianities can also be created after inflation through tachyonic preheating at the end of inflation [245, 570, 578]. Preheating of light fields after inflation has also been considered in [243, 244, 246], and in δN formalism [247, 579]. It was found that the λφ 4 model can lead to levels of non-Gaussianities that are already on the verge of being excluded by current observations [243]. Also, very recently, it was pointed out that the waterfall part of the dynamics in a generic non-SUSY hybrid type inflation (or hilltop inflation) with a potential of the generic form 

<img src='content_image/349477.jpg'>

could generate a large amount of non-Gaussian fluctuations given by [580] $^{54}$. 

<img src='content_image/349478.jpg'>

where the index e denotes the end of inflation and γ is a semi-analytic parameter in the range [0 . 03 − 0 . 1]. 

## 6. Challenges for non-SUSY models 

For non-SUSY models of inflation there are two more challenges related at the classical and the quantum level. 

• Effective couplings and symmetries: 

At the classical level inflaton can couple to other light scalar fields during inflation. In any of the effective potentials considered so far, there is no symmetry argument which 

