Messenger inflation in gauge mediation and superWIMP dark matter

We discuss phenomenological viability of a novel inflationary model in the minimal gauge mediated supersymmetry breaking scenario. In this model, cosmic inflation is realized in the flat direction along the messenger supermultiplets and a natural dark matter candidate is the gravitino from the out-of-equilibrium decay of the bino-like neutralino at late times, which is called the superWIMP scenario. The produced gravitino is warmish and can have a large free-streaming length; thus the cusp anomaly in the small scale structure formation may be mitigated. We show that the requirement of the Standard Model Higgs boson mass to be $m_{h^0}=125.1$ GeV gives a relation between the spectrum of the cosmic microwave background and the messenger mass $M$. We find, for the e-folding number $N_e=60$, the Planck 2018 constraints (TT, TE, EE+lowE+lensing+BK15+BAO, 68% confidence level) give $M > 3.64\times 10^7$ GeV. The gravitino dark matter mass is $m_{3/2} < 5.8$ GeV and the supersymmetry breaking scale $\Lambda$ is found to be in the range $(1.28-1.33)\times 10^6$ GeV. Future CMB observation is expected to give tighter constraints on these parameters.