Big Bang, dark energy and dark matter are the main ingredients of the governing paradigm of astrophysics today. The scenario, however, faces several substantial question marks, such as the cause of the Big Bang singularity, the sudden inflationary expansion and the consistence of dark matter. There are also divergent theories about the origin of dark energy. A new theory, CBU standing for the Continuously Breeding Universe, has been developed in order to find solutions based on known principles of physics. The theory incorporates important ideas from the past. The universe is considered as a complex emerging system, which starts from the single fluctuation of a positron-electron pair. Expansion is driven by the appearance of new pairs, which “stay alive” due to a Planck time far larger than the period between fluctuations. It is shown that the gravitational potential energy is the negative counterpart that balances the increase of energy due to new matter. The gravitational parameter G (Newton’s gravitational constant) is inversely proportional to the Einsteinian curvature radius r. As a result the Planck length and Planck time t_P are dependent of the curvature and hence by the size of the universe. Here we show that the solution to the Schrödinger equation of an initial positron-electron fluctuation includes an exponential function parameter equal to the Planck length as determined by definition. This gives a strong argument in favour of the CBU theory. Further, the existence of a wave function of the initial event provides a link between quantum mechanics and the theory of general relativity. The universe is a macroscopic manifestation of the quantum world.

general relativity, positron-electron vacuum fluctuation, Schrödinger equation, Planck scales, dark energy