  The primordial Universe might be highly inhomogeneous. We perform the 3+1D
Numerical Relativity simulation for the evolution of scalar field in an initial
inhomogeneous expanding Universe, and investigate how it populates the
landscape with both de Sitter (dS) and AdS vacua. The simulation results show
that eventually either the field in different region separates into different
vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding
but the spacetime inside AdS bubbles is contracting) come into being with clear
bounderies, or overall region is dS expanding with a few smaller AdS bubbles
(which collapsed into black holes) or inhomogeneously collapsing.
