Gravity mediation without a Polonyi problem
  Recent indications of the 125GeV Higgs at the LHC can be explained in a relatively high-scale SUSY scenario where the sparticle masses are multi-TeV as is realized in the focus-point region. However, it suffers from the notorious cosmological Polonyi problem. We argue that the Polonyi problem is solved and thermal or non-thermal leptogenesis scenario works successfully, if a certain Polonyi coupling to the inflaton is enhanced by a factor of 10-100. 
Kazunori Nakayama, Fuminobu Takahashi, Tsutomu T. Yanagida
hep-ph hep-th