Minimal model of gravitino dark matter

Motivated by the absence of signals of new physics in searches for both new particles at the LHC and a weakly interacting massive particle dark matter candidate, we consider a scenario where supersymmetry is broken at a scale above the reheating temperature. The low-energy particle content then only consists of Standard Model states and a gravitino. We investigate the possibility that the latter provides the main component of dark matter through the annihilation of thermalized Standard Model particles. We focus on the case where its production through scattering in the thermal plasma is well approximated by the nonlinear supersymmetric effective Lagrangian of the associated Goldstino and identify the parameter space allowed by the cosmological constraints, allowing the possibility of a large reheating temperature compatible with leptogenesis scenarios and alleviating the so-called “gravitino problem”.

Figure 1

Region in the parameter space ($m_{3/2}$; $T_{\mathrm{RH}}$) respecting the relic abundance constraint [49, 50] from Eq. (16). The points above the black line are excluded because the gravitino would overclose the Universe. The blue line shows the constraint from the Higgs mass with an observed value of 125 GeV, which sets an upper limit for the scale of supersymmetry breaking [Eq. (4)].

Figure 2

The parameter space for $M_{\mathrm{NLSP}}$. It must be lower than $\sqrt{F}$. The blue line corresponds to $n_g⟨\sigma v{⟩}_{gg\to \tilde{g}\tilde{g}}=H$. Below the line, the NLSP is still in equilibrium and can decay to a gravitino.