Can Higgs Inflation be Saved with High-scale Supersymmetry ?

It is shown whether Higgs inflation can be saved with high-scale supersymmetry critically depends on the magnitude of non-minimal coupling constant $\xi$. For small $\xi \le 500$, the threshold correction at scale $M_P\mathrm{/}\xi$ is constrained in high precision.Its magnitude is in the narrow range of $(-0.03,-0.02)$ and $(-0.05,-0.04)$ for the wino and higgsino/singlino dark matter, respectively. While in the large $\xi$-region with $\xi \ge {10}^4$, such high-scale supersymmetry is excluded by too large threshold correction as required by Higgs inflation.