Case for an EeV Gravitino.

We consider the possibility that supersymmetry is broken above the inflationary mass scale and that the only "low" energy remnant of supersymmetry is the gravitino with a mass of the order of the EeV scale. The gravitino in this class of models becomes a candidate for the dark matter of the Universe. To avoid the overproduction of gravitinos from the decays of the next-to-lightest supersymmetric particle we argue that the supersymmetric spectrum must lie above the inflationary mass scale (M_{SUSY}>10^{-5}M_{P}∼10^{13} GeV). Since m_{3/2}≃M_{SUSY}^{2}/M_{P}, we expect m_{3/2}≳0.2 EeV. Cosmological constraints then predict a relatively large reheating temperature between 10^{10} and 10^{12} GeV.

Grand unified theory precursors and nontrivial fixed points in higher-dimensional gauge theories.

Within the context of traditional logarithmic grand unification at M(GUT) approximately equal to 10(16) GeV, we show that it is nevertheless possible to observe certain GUT states such as X and Y gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as "GUT precursors." These states offer an interesting alternative possibility for new physics at the TeV scale, and could be used to directly probe GUT physics even though the scale of gauge coupling unification remains high. Our results also give rise to a Kaluza-Klein realization of nontrivial fixed points in higher-dimensional gauge theories.