Paper detail

Susy Seesaw Inflation and NMSO(10)GUT

We show that Supersymmetric models with Type I seesaw neutrino masses support slow roll inflection point inflation. The inflaton is the D-flat direction labelled by the chiral invariant HLN composed of the Higgs(H), slepton(L) and conjugate sneutrino(N) superfields. The scale of inflation and fine tuning is set by the conjugate neutrino Majorana mass $M_{ν^c} \sim 10^6-10^{12}$ GeV. The cubic term in the (quartic) inflaton potential is dominantly from superpotential (not soft Susy breaking) couplings. The tuning conditions are thus insensitive to soft supersymmetry breaking parameters and are generically much less stringent than for previous `A-term' inflation scenarios controlled by mass scales $\sim TeV$. WMAP limits on the ratio of tensor to scalar perturbations limit the scale $M$ controlling inflection point inflation: $M <7.9 \times 10^{13}$ GeV. `Instant preheating' is operative and dumps the inflaton energy into MSSM modes giving a high reheat temperature : $T_{rh} \approx M_{ν^c}^{3/4}\, 10^{6}$ GeV $\sim 10^{11}- 10^{15} $ GeV. A large gravitino mass $> 50 $ TeV is therefore required to avoid over closure by reheat produced gravitinos. `Instant preheating' and NLH inflaton facilitate production of right handed neutrinos during inflaton decay and thus non-thermal leptogenesis in addition to thermal leptogenesis. We show that the embedding in the fully realistic New Minimal Supersymmetric SO(10) GUT requires use of the heaviest righthanded neutrino mass as the controlling scale but the possibility of a measurable tensor scalar perturbation ratio seems marginal. We examine the parametric difficulties remaining.