Gauge mediation in supergravity and gravitino dark matter

Gravitinos and hidden sector fields often cause a cosmological disaster in supersymmetric models. We find that a model with gravitational gauge mediation solves such a problem quite naturally. The $\mu$-problem is also absent in the model. Moreover, the abundance of gravitinos explains correct amount of dark matter of the universe. The dark matter abundance can be calculated without detailed information on the thermal history of the universe such as the reheating temperature after inflation.

Figure 1

A typical evolution of the $S$ field (left) and time dependence of the amplitude $|S|$ (right) for $m_S=400\mathrm{GeV}$, $m_{3/2}=500\mathrm{MeV}$ and $\lambda ={10}^{-3}$.

Figure 2

The parameter regions of the model ($N=1$) which account for the dark matter component of the universe. The correct amount of gravitino dark matter can be obtained within the allowed range of parameter space. Below the dot-dashed line in the left figure, the decay mode of $S$ into two Higgs boson is closed [Case (B)]. The constraint from the lower bound on the decay temperature $T_d>2\mathrm{MeV}$ is indicated. The contour of $T_d=5\mathrm{MeV}$ is also shown. In the right figure, the decay mode $S\to hh$ is open above the dot-dashed line [Case (A)]. The decay mode into two Binos is open in the right-lower region.