We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of volume of the Universe in a state with a given density $\rho$ at any given moment of proper time $t$ is concentrated near the centers of deep exponentially wide spherically symmetric wells in the density distribution. Since this statement is very surprising and counterintuitive, we perform our investigation by three different analytical methods to verify our conclusions, and then confirm our analytical results by computer simulations. If one assumes that we are typical observers living in the Universe at a given moment of time, then our results may imply that we should live near the center of a deep and exponentially large void, which we will call an infloid. The validity of this particular interpretation of our results is not quite clear since it depends on the as-yet unsolved problem of measure in quantum cosmology. Therefore, at the moment we would prefer to consider our results simply as a demonstration of nontrivial properties of the hypersurface of a given time in the fractal self-reproducing universe, without making any far-reaching conclusions concerning the structure of our own part of the Universe. Still we believe that our results may be of some importance since they demonstrate that nonperturbative effects in quantum cosmology, at least in principle, may have significant observational consequences, including an apparent violation of the Copernican principle.

• Received 4 January 1996

DOI:https://doi.org/10.1103/PhysRevD.54.2504