0 0.05 0.1 0.15 0.2 0.25 0.3 m$_{Ν}$ GLYPH<LParen1> eV GLYPH<RParen1> 0 5 10 15 20 25 m Φ GLYPH<LParen1> GeV GLYPH<RParen1> FIG. 10: The inflaton mass m$_{φ}$ is plotted as a function of the neutrino mass m$_{ν}$ [716]. For various reasons, which will become clear, the inclusion of a gauge symmetry under which the RH (s)neutrinos are not singlet is crucial. As far as inflation is concerned, a singlet RH sneutrino would not form a gauge-invariant inflaton along with the Higgs and slepton fields. The simplest extension of the SM symmetry, SU (3)$_{C}$ × SU (2)$_{L}$ × U (1)$_{Y}$ × U $^{(1)$_{B}$}$− $_{L}$, which is also well motivated: anomaly cancelation requires that three RH neutrinos exist, so that they pair with LH neutrinos to form three Dirac fermions. The relevant superpotential term is Here N , L and H$_{u}$ are superfields containing the RH neutrinos, left-handed (LH) leptons and the Higgs which gives mass to the up-type quarks, respectively. In this model there is an extra Z boson ( Z ′ ) and one extra gaugino ( ˜ Z ′ ). The U $^{(1)$_{B}$}$− L gets broken around TeV by new Higgs fields with B − L = ± 1. This also prohibits a Majorana mass for the RH neutrinos at the renormalizable level (note that NN has B − L = 2). The Majorana mass can be induced by a non-renormalizable operator, but it will be very small. The value of h needs to be small, i.e. h ≤ 10 − $^{12}$, in order to explain the light neutrino mass, ∼ O (0 . 1 eV) corresponding to the atmospheric neutrino oscillations detected by Super- Kamiokande experiment. Note that the NH$_{u}$L monomial represents a D -flat direction under the U $^{(1)$_{B}$}$− $_{L}$, as well as the SM gauge group [88, 716]. where ˜ N , ˜ L , H$_{u}$ are the scalar components of corresponding superfields. Since the RH 152 W ⊃ hNH$_{u}$L. (333) φ = ˜ N + H$_{u}$ + ˜ L √$_{3}$ , (334)