Low-energy supersymmetry breaking without the gravitino problem

In models of low-energy gauge mediation, the observed Higgs mass is in tension with the cosmological limit on the gravitino mass ${m}_{3/2}\ensuremath{\lesssim}16\text{ }\text{ }\mathrm{eV}$. We present an alternative mediation mechanism of supersymmetry breaking via a $U(1)$ $D$ term with an ${E}_{6}$-inspired particle content, which we call vector mediation. The gravitino mass can be in the eV range. The sfermion masses are at the 10 TeV scale, while gauginos are around a TeV. This mechanism also greatly ameliorates the $\ensuremath{\mu}$ problem.