  In theories with extra dimensions, the cosmological hierarchy problem can be
thought of as the unnaturally large radius of the observable universe in
Kaluza-Klein units. We sketch a dynamical mechanism that relaxes this. In the
early universe scenario we propose, three large spatial dimensions arise
through tunneling from a 'cosmic egg', an effectively one-dimensional
configuration with all spatial dimensions compact and of comparable, small
size. If the string landscape is dominated by low-dimensional
compactifications, cosmic eggs would be natural initial conditions for
cosmology. A quantum cosmological treatment of a toy model egg predicts that,
in a variant of the Hartle-Hawking state, cosmic eggs break to form higher
dimensional universes with a small, but positive cosmological constant or
quintessence energy. Hence cosmic egg cosmology yields a scenario in which the
seemingly unnaturally small observed value of the vacuum energy can arise from
natural initial conditions.
