  In quantum cosmology the DeWitt boundary condition is a proposal to set the
wave function of the universe to vanish at the classical big-bang singularity.
In this Letter, we show that in many gravitational theories including general
relativity, the DeWitt wave function does not take a desired form once tensor
perturbations around a homogeneous and isotropic closed universe are taken into
account: anisotropies and inhomogeneities due to the perturbations are not
suppressed near the classical singularity. We then show that
Ho\v{r}ava-Lifshitz gravity provides a satisfactory DeWitt wave function. In
particular, in the limit of $z=3$ anisotropic scaling, we find an exact
analytic expression for the DeWitt wave function of the universe with
scale-invariant perturbations. In general cases with relevant deformations, we
show that the DeWitt wave function can be systematically expanded around the
classical big-bang singularity with perturbations under control.
