content_image/370638.jpg content_image/370641.jpg
given by: W = κS ( ZZ − M 2 $_{1}$), while in the second brane W = κS ( φφ − M 2 $_{2}$), where φ, φ belong to ( ¯ 4 , 1 , 2 ) and ( 4 , 1 , 2 ) [696]. Similar constructions were made in Ref. [77] where on one brane SU (5) × U (1)$_{X}$ and on the other SU (5) ′ × U (1) ′ X were preserved, inflationary potential arises to the breaking of U (1) at a scale close to the GUT scale. 

In all the above examples, see Refs. [67, 70, 76, 77, 83, 692, 696, 701], it is possible to excite non-thermal leptogenesis either from the direct decay of the inflaton or the Higgs coupled to it or from non-perturbative excitation from the coherent oscillations of the inflaton. 

## 6. Inflation, neutrino sector and family replication 

The right handed Majorana sneutrino as an inflaton has been proposed as a particle physics candidate for inflation [505, 702]. These initial models were based on a chaotic type potential for the inflaton with a superpotential 72 

<img src='content_image/370638.jpg'>

where the right handed Majorana neutrino superfield, N , has been treated as a gauge sin- glet. In order to avoid higher order contributions such as N 3 term in the superpotential, the right handed neutrino can be assigned odd under R-parity. The lightest right handed electron sneutrino acts as an inflaton with an initial VEV larger than M$_{P}$ . After the end of inflation the coherent oscillations of the sneutrino field generates lepton asymmetry with the interference between tree-level and one-loop diagrams. The largest lepton asymme- try is proportional to the reheat temperature, n$_{L}$/s ∼ ϵ (3 T$_{R}$/ 4 M$_{P}$ ). The CP asymmetry, ϵ ∼ (ln 2 / 8 π )Im h ∗ 2 $_{33}$. Models of inflation and non-thermal leptogenesis were also considered in Refs. [339, 703, 704]. 

Sneutrino hybrid inflation was constructed in Refs. [79, 80]. In [79] the following super- potential has been used to generate inflation and the masses for the right handed neutrinos: 

<img src='content_image/370641.jpg'>

where κ, ( λ$_{N}$ )$_{ij}$ are dimensionless Yukawa couplings, M, M ′ $^{, M}$∗ are three independent mass scales. Φ , S, N are all gauge singlets. The waterfield is Φ generates masses for the right 

