Universality in Pure Gravity Mediation

If low energy supersymmetry is realized in nature, the apparent discovery of a Higgs boson with mass around 125 GeV points to a supersymmetric mass spectrum in the TeV or multi-TeV range. Multi-TeV scalar masses are a necessary component of supersymmetric models with pure gravity mediation or in any model with strong moduli stabilization. Here, we show that full scalar mass universality remains viable as long as the ratio of Higgs vevs, tan beta is relatively small (\lesssim 2.5). We discuss in detail the low energy (observable) consequences of these models.