content_image/362356.jpg content_image/362357.jpg content_image/362358.jpg
where λ ∼ O (1). Therefore, exciting the SM gauge bosons and the SM fermions through parametric resonance of a gauge singlet inflaton is a daunting task. Inflaton would rather prefer perturbative decay $^{81}$. 

## 5. Fragmentation of the inflaton 

One very curious aspect of fermionic coupling to the inflaton is fragmentation of the inflaton to form an inflating non-topological solitons, known as Q-balls $^{82}$. Let us illustrate this idea by studying a chaotic inflation model where the inflaton field is not real but complex. Provided the fermions live in a larger representation than the bosons, the inflaton mass obtains a Logarithmic correction $^{83}$: 

where the value of K is determined by the Yukawa coupling h with K = − C ( h $^{2}$/ 16 π $^{2}$), where C is some number. If K < 0, the inflaton condensate feels a negative pressure for field values φ ≪ M , we find: 

<img src='content_image/362356.jpg'>

<img src='content_image/362357.jpg'>

where we assume | K | ≪ 1. The equation of state for a field rotating in such a potential is 

<img src='content_image/362358.jpg'>

where p and ρ is a pressure and energy density of the scalar field, respectively. Evidently, the negative value of K corresponds to the negative pressure, which signals the instability 

