On possible wave structures of the universe (the spontaneous violation of the cosmological principle)

Recent redshift surveys reveal large structures of galaxies with sizes in excess of 100 h-1 Mpc. These structures appear to be two-dimensional sheets (''walls''), perhaps periodically spaced. Here we propose that these ''walls'' are the manifestation of a spontaneous breaking of the symmetry implied by the Cosmological Principle. We present a model of a Robertson-Walker universe where the geometry of the large scale matter-distribution is determined by the most symmetric eigenmode Yn,0,0 of S3. This model reproduces the geometry of the observed large scale structures for an appropriate choice of the center of vibration and wavelength of the eigenmode Yn,00. We also formulate predictions on the distribution of galaxies that should be observed as soon as new deep and wide-angle redshift surveys will become available. The observation of the predicted wave structures would confirm our model, which in turn could have far reaching consequences for cosmology and also for physics. In fact, as shown by Fock in 1935, the most symmetric eigenfunction of the Hydrogen atom represented in momentum space is the same Yn,0,0. (author). 25 refs, 7 figs