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 $\xi \leq 500$, the threshold correction at scale $M_{P}/\xi$ 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 $\xi \geq 10^{4}$, such high-scale supersymmetry is excluded by too large threshold correction as required by Higgs inflation.