  In hep-th/0506040 we discussed a classically constrained model of gravity.
This theory contains known solutions of General Relativity (GR), and admits
solutions that are absent in GR. Here we study cosmological implications of
some of these new solutions. We show that a spatially-flat de Sitter universe
can be created from ``nothing''. This universe has boundaries, and its total
energy equals to zero. Although the probability to create such a universe is
exponentially suppressed, it favors initial conditions suitable for inflation.
Then we discuss a finite-energy solution with a nonzero cosmological constant
and zero space-time curvature. There is no tunneling suppression to fluctuate
into this state. We show that for a positive cosmological constant this state
is unstable -- it can rapidly transition to a de Sitter universe providing a
new unsuppressed channel for inflation. For a negative cosmological constant
the space-time flat solutions is stable.
