Current Issues for Inflation

Most inflation models create a lot of gravitinos I will focus on papers that appeared in 1999, building on a fairly comprehensive review 1 of earlier work, and starting with gravitino creation. Gravitinos are created at reheating by thermal collisions . If the gravitino mass m3/2 is of order 100GeV, as in gravity-mediated models of SUSY breaking, these gravitinos upset nucleosynthesis unless γTR ∼ < 10 9 GeV, where TR is the reheat temperature, and γ is the increase in entropy per comoving volume (if any) between reheating and nucleosynthesis. If instead m3/2 ∼ 100 keV, an in typical gauge-mediated models of SUSY breaking, the gravitino is stable and will overclose the Universe unless γTR ∼ < 10 4 GeV. Only if m3/2 ∼ > 60TeV, as might be the case in anomaly-mediated models of SUSY breaking, are the gravitinos from thermal collisions completely harmless. Gravitinos will also be created after inflation , by the amplification of the vacuum fluctuation. The evolution equations for the helicity 1/2 and 3/2 mode functions, required to calculate this second effect, have been presented only this year. A suitably chosen helicity 3/2 mode function satisfies 4 the Dirac equation in curved spacetime, with mass m3/2(t) (the gravitino mass in the background of the time-dependent scalar field(s) which dominate the Universe after inflation). This implies that helicity 3/2 gravitinos created from the vacuum are cosmologically insignificant, compared with those created from particle collisions . The situation for helicity 1/2 is more complicated, because this state mixes with the fermions involved in SUSY breaking (the super-Higgs effect). So far, the evolution equation for the mode function has been presented 5,6 only for the simplest possible case, that the only relevant superfield is a single chiral superfield. Using this idealized equation, its authors estimated (see also ) that gravitinos created just after inflation have, at nucleosynthesis, the abundance n s ≃ 10 γTRM 3 V . (1)