  We analyze the spectrum of time observable in noncommutative cosmological
model introduced in [5], defined by $(\rho, s=\frac 12)\,$ representation of
the de Sitter group. We find that time has peculiar property: it is not
self-adjoint, but appropriate restrictions to the space of physical states give
self-adjoint extensions. Extensions have discrete spectrum with logarithmic
distribution of eigenvalues, $\,t_n \sim \ell\, \log\, n$+const, where $\ell$
characterizes noncommutativity and the usual assumption is
$\,\ell=\ell_{Planck}$. When calculated on physical states, radius of the
universe is bounded below by $\, \ell\, \sqrt{\frac 34\, \left( \frac 14
+\rho^2\right)}\, $, which resolves the big bang singularity. An immediate
consequence of the model is a specific breaking of the original symmetry at the
Planck scale.
