Non-universalities in pure gravity mediation

The simplest model of pure gravity mediation contains only two free parameters: the gravitino mass and tan beta. Scalar masses are universal at some high energy renormalization scale and gaugino masses are determined through anomalies and depend on the gravitino mass and the gauge couplings. This theory requires a relatively large gravitino mass (m(3/2) greater than or similar to 300 TeV) and a limited range in tan beta similar or equal to 1.7-2.5. Here we generalize the theory to allow for non-universality in the Higgs soft masses. This introduces zero, one or two new free parameters associated with Higgs soft masses. This generalization allows us to greatly increase the allowed range in tan beta and it allows one to find viable solutions with lower m(3/2). The latter is important if we hope to find a low energy signal from gluinos. Some special cases of these non-universalities are suggestive of Higgs bosons as Nambu-Goldstone bosons or a partial no-scale structure for the Higgs doublets. Thus, we probe signatures at the weak scale and structures at the GUT and/or Planck scale.