Cosmological constraints on a Peccei-Quinn flatino as the lightest supersymmetric particle

In an interesting class of models, non-renormalizable terms of the superpotential are responsible for the spontanteous breaking of Peccei-Quinn (PQ) symmetry as well as the generation of the $\mu$ term. The flaton fields which break PQ symmetry are accompanied by flatinos, and the lightest flatino (the LSP) can be the stable, while the decay of the lightest neutralino (the NLSP) might be visible at colliders with a low axion scale. We examine the cosmology of these models, involving thermal inflation just after the PQ phase transition. The branching ratio of flatons into axions must be small so as not to interfere with nucleosynthesis, and flatons must not decay into the LSP or it will be over-abundant. We explore a simple model,with light flatons which can decay into $Z$ or $W$ bosons, or into a light Higgs ($h^0$) plus a $Z$ boson, to show that such features can be realized in a wide range of parameter space. The mass of the NLSP can be as low as $(m_{h^0}+m_Z)/2$, with an axion scale of order $10^{10}$ GeV and a final reheat temperature typically of order $10\GeV$. Then, the flatino LSP is a good dark matter candidate because the reheat temperature can be high enough to allow its production from the decay of the thermalized LSP, while low enough to prevent its overproduction from the decay of sfermions.