Tunneling Newtonian Universe

We analyze quantum-mechanical counterpart of Newtonian cosmology and show that effects of zero-point motion eliminate classical density singularity. Quantum effects are particularly significant for closed Universes where without the cosmological constant the energy spectrum and space curvature are quantized. When small positive cosmological constant is included, these states become quasi-stationary and decay via tunneling. Corresponding metastable Universes evolve in three stages: long period of gestation followed by rapid tunneling expansion further followed by slower Hubble expansion. This closely resembles inflation scenario of modern cosmology.