Relativistic Violation Invariance, Multiverses and Quantum Field Theory

The possibility of interaction among multiverses is studied assuming that in the first instants of the big-bang, many disjoint regions were created producing many independent universes (multiverses). Many of these mini-universes were unstable and they decayed, but other remained as topological remnant (like domain walls or baby universes) or possibly as mini-black-holes. In this paper, we study the quantum statistical mechanics of multiverses assuming that in the first instants of the big-bang, the relativistic symmetry was only an approximate symmetry and the interaction among multiverses was produced by non-local communication. As a warm-up, in the first part of this paper we study the statistical quantum mechanics of generally covariant systems (particles, strings and membranes) living on noncommutative spaces. In the second part, the non-local communication is implemented by noncommutativity in the fields space and the possible physical implications in cosmology are considered. As the Lorentz symmetry is broken, technically the problem is solved assuming a privileged reference frame containing the multiverses, i.e. a kind of ideal quantum gas in a reservoir. If the reservoir is very large, then one can consider a uniform multiverses distribution and approximate each multiverse as tensionless p-brane. The breaking of the relativistic symmetry induces on each multiverse a tiny harmonic interaction. The oscillation frequency for each multiverse is proportional to 1/B, where B is the noncommutativity parameter. We argue that B can identified as the primordial magnetic field, i.e. ∼ 10−16 GeV. In this model of multiverses, each multiverse interacts with other neighbour multiverses in a similar way as atoms do in the Einstein model for the specific heat of a solid. In this case, the analogous of the phonon is played by quantums with energy equal to B. Each neighbour multiverse should have a pulsation frequency Ω ∼ 10−63 s−1. This tiny frequency could suggest that the relativistics invariance –from the cosmological point of view– is almost exact and the multiverses could be not detected using the presently astronomical observations.