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 $m_{3/2}\lesssim 16\mathrm{eV}$. 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 $\mu$ problem.