Abstract
The goal of this contribution is to present the properties of a class of quantum bouncing models in which the quantum bounce originates from the Dirac canonical quantization of a midi-superspace model composed of a homogeneous and isotropic background, together with small inhomogeneous perturbations. The resulting Wheeler-DeWitt equation is interpreted in the framework of the de Broglie-Bohm quantum theory, enormously simplifying the calculations, conceptually and technically. It is shown that the resulting models are stable and they never get to close to the Planck energy, where another more involved quantization scheme would have to be evoked, and they are compatible with present observations. Some physical effects around the bounce are discussed, like baryogenesis and magnetogenesis, and the crucial role of dark matter and dark energy is also studied.
Highlights
Cosmological observations strongly indicate that the Universe is expanding from a very hot era, when the geometry of space was highly homogeneous and isotropic, with tiny deviations from this special symmetric state.Cosmology is a very peculiar part of Physics, because the physical system under investigation is the Universe as a whole, and one cannot control its initial conditions, as in other physical situations
They are obtained using a simple quantization procedure, with the compromise that the resulting models never get to close to Planck energy, where other more involved quantization schemes should have to be used: Dirac canonical quantization of a midisuperspace model composed of a inhomogeneous and isotropic background, together with small homogeneous perturbations
The results were obtained in the framework of the de Broglie-Bohm quantum theory, turning out to enormously simplify the calculations, conceptually and technically
Summary
Cosmological observations (the cosmic microwave background radiation [1], Big Bang nucleosynthesis [2], large scale structure [3] and cosmological red-shift [4]) strongly indicate that the Universe is expanding from a very hot era, when the geometry of space was highly homogeneous and isotropic (maximally symmetric space-like hyper-surfaces), with tiny deviations from this special symmetric state. When the inflaton field does not satisfy the strong energy condition (ρ + 3p ≥ 0, ρ + p ≥ 0, where p is the pressure), which is a commonplace feature of field theories, the expansion is accelerated, a/a > 0, and the problems arising from Equations (1) and (2) are overcome During this phase, called inflation [19,20,21], it is possible that a increases faster than RH, see Equation (1), and, looking backwards in time, scales of cosmological interest were smaller than the Hubble radius in this era, allowing causal contact, and avoiding the horizon problem and the structure formation issue. I will end up in Section 7, with conclusions and discussions
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