Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics

Abstract

Every physical theory involving quantum fields requires a model of quantum vacuum. The vacuum associated to quantum gravity must incorporate the prescriptions from both the theory of relativity and quantum physics. In this work, starting from the hypothesis of nucleation of sub-Planckian bubbles from a de Sitter vacuum, we study the necessary conditions to obtain baby universes, black holes and particles. The de Sitter-Planck background is described by an “infinite” Quantum Boltzmann statistics that generates fermions and bosons, and manifests itself as a deformation of the geometry that leads to a generalized uncertainty principle, a unified expression for the generalized Compton wavelength and event horizon size, drawing a connection between quantum black holes and elementary particles, seen as a collective organization of the bubbles of the vacuum described by the generalized Compton wavelength. The quantum thermodynamics of black holes is then outlined and the physical history of each bubble is found to depend on the cosmological constant described in terms of thermodynamic pressure. A treatment of the Casimir effect is provided in the de Sitter-Planck background, and finally wormholes are explored as bubble coalescence processes.