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We investigate Planck scale boundary conditions on the Higgs sector of thestandard model with a gauge singlet scalar dark matter. We will find thatvanishing self-coupling and Veltman condition at the Planck scale are realizedwith the 126 GeV Higgs mass and top pole mass, 172 GeV $\lesssim M_t\lesssim$173.5 GeV, where a correct abundance of scalar dark matter is obtained withmass of 300 GeV $\lesssim m_S \lesssim$ 1 TeV. It means that the Higgspotential is flat at the Planck scale, and this situation can not be realizedin the standard model with the top pole mass.

Planck scale boundary conditions in the standard model with singlet scalar dark matter