Supersymmetric Seesaw Inflation
  Supersymmetric Unified theories which incorporate a renormalizable Type I
seesaw mechanism for small neutrino masses can also provide slow roll
inflection point inflation along a flat direction associated with a gauge
invariant combination of the Higgs, slepton and right handed sneutrino
superfields. Inflationary parameters are related to the Majorana and Dirac
couplings responsible for neutrino masses with the scale of inflation set by a
right-handed neutrino mass $M_{\nu^c} \sim 10^6-10^{12}$ GeV. Tuning of the
neutrino Dirac and Majorana superpotential couplings and soft Susy breaking
parameters is required to enforce flatness of the inflationary potential. In
contrast to previous inflection point inflation models the cubic term is
dominantly derived from superpotential couplings rather than soft A-terms. Thus
since $M_{\nu^c}>>M_{Susy}$ the tuning condition is almost independent of the
soft supersymmetry breaking parameters and therefore more stable. The required
fine tuning is also less stringent than for Minimal SUSY Standard Model (MSSM)
inflation or Dirac neutrino 'A-term" inflation scenarios due to the much larger
value of the inflaton mass. Reheating proceeds via `instant preheating' which
rapidly dumps all the inflaton energy into a MSSM mode radiation bath giving a
high reheat temperature $T_{rh} \approx M_{\nu^c}^{3/4}\, 10^{6}$ GeV $\sim
10^{11}- 10^{15} $ GeV.
  Thus our scenario requires large gravitino mass $> 50 $ TeV to avoid a
gravitino problem. The `instant preheating' and Higgs component of the inflaton
also imply a `non-thermal' contribution to Leptogenesis due to facilitated
production of right handed neutrinos during inflaton decay. We derive the
tuning conditions for the scenario to work in the realistic New Minimal
Supersymmetric SO(10) GUT and show that they can be satisfied by realistic
fits.
