Gravitino or Axino Dark Matter with Reheat Temperature as high as $10^{16}$ GeV

A new scheme for lightest supersymmetric particle (LSP) dark matter is introduced and studied in theories of TeV supersymmetry with a QCD axion, $a$, and a high reheat temperature after inflation, $T_R$. A large overproduction of axinos ($\tilde{a}$) and gravitinos ($\tilde{G}$) from scattering at $T_R$, and from freeze-in at the TeV scale, is diluted by the late decay of a saxion condensate that arises from inflation. The two lightest superpartners are $\tilde{a}$, with mass of order the TeV scale, and $\tilde{G}$ with mass $m_{3/2}$ anywhere between the keV and TeV scales, depending on the mediation scale of supersymmetry breaking. Dark matter contains both warm and cold components: for $\tilde{G}$ LSP the warm component arises from $\tilde{a} \rightarrow \tilde{G}a$, while for $\tilde{a}$ LSP the warm component arises from $\tilde{G} \rightarrow \tilde{a}a$. The free-streaming scale for the warm component is predicted to be of order 1 Mpc (and independent of $m_{3/2}$ in the case of $\tilde{G}$ LSP). $T_R$ can be as high as $10^{16}$ GeV, for any value of $m_{3/2}$, solving the gravitino problem. The PQ symmetry breaking scale $V_{PQ}$ depends on $T_R$ and $m_{3/2}$ and can be anywhere in the range $(10^{10} - 10^{16})$ GeV. Detailed predictions are made for the lifetime of the neutralino LOSP decaying to $\tilde{a}+ h/Z$ and $\tilde{G}+h/Z/\gamma$, which is in the range of $(10^{-1}-10^6)$m over much of parameter space. For an axion misalignment angle of order unity, the axion contribution to dark matter is sub-dominant, except when $V_{PQ}$ approaches $10^{16}$ GeV.