NONPERTURBATIVE AMPLIFICATION OF INHOMOGENEITIES IN A SELF-REPRODUCING UNIVERSE

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 give n moment of proper time t is concentrated near the centers of deep exp onentially wide spherically symmetric wells in the density distributio n. Since this statement is very surprising and counterintuitive, we pe rform our investigation by three different analytical methods to verif y our conclusions, and then confirm our analytical results by computer simulations. If one assumes that we are typical observers living in t he 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 inter pretation of our results is not quite clear since it depends on the as -yet unsolved problem of measure in quantum cosmology. Therefore! at t he moment we would prefer to consider our results simply as a demonstr ation 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 the y demonstrate that nonperturbative effects in quantum cosmology, at le ast in principle, may have significant observational consequences, inc luding an apparent violation of the Copernican principle.