THE SPONTANEOUS VIOLATION OF THE COSMOLOGICAL PRINCIPLE AND THE POSSIBLE WAVE STRUCTURES OF THE UNIVERSE

Recent redshift surveys reveal large structures of galaxies with sizes in excess of 100 h(-1) Mpc. These structures appear to be two-dimensi onal sheets (''walls'') that are perhaps periodically spaced. Here we propose that these ''walls'' are the manifestation of a spontaneous br eaking of the symmetry implied by the cosmological principle. We prese nt a model of a Robertson-Walker universe where the geometry of the la rge-scale matter-distribution is determined by the most symmetric eige nmode Y-n,Y-0,Y-0 of S-3. This model reproduces the geometry of the ob served large-scale structures for an appropriate choice of the center of vibration and wavelength of the eigenmode Y-n,Y-0,Y-0. We also form ulate predictions on the distribution of galaxies that should be obser ved as soon as new deep and wide-angle redshift surveys will become av ailable. The observation of the predicted wave structures would confir m our model, which in turn could have far-reaching consequences for co smology and also for physics. In fact, as shown by Fock in 1935, the m ost symmetric eigenfunction of the hydrogen atom represented in moment um space is the same Y-n,Y-0,Y-0.