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Register a new userQuantum Mixmaster as a model of the Primordial Universe
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The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl-Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined.
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In a primordial universe pre(post)-inflationary era , there could be phases of early universe made of cold gas baryons, radiation and early post inflationary cosmological constant. I showed that in the baryonic epoch, the quantum vacuum is unique. By using the standard quantization scheme for a massive minimally coupled scalar field with maximal conformal symmetry in the classical spacetime, I demonstrated that the scalar modes had an effective mass $m_{eff}^2approx 0$ (or $m_{eff}^2approx constant$). This argument validated when the conformal time $eta$ kept so close to the inflation ending time $eta=eta_c$. The energy density of the baryonic matter diverged at the inflation border and vanishes at the late time future. Furthermore I argued that at very early accelerating epoch when the radiation was the dominant part in the close competition with the early time cosmological constant, fine tuned mass of the scalar field $mpropto sqrt{Lambda}$ also provided a unique quantum vacuum. The reason is that the effective mass eventually is vanished. A remarkable observation was that all the other possible vacuum states squeezed eternally.
The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark components open. Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity. The spatially averaged 3+1 Einstein equations are effective balance equations that need a closure condition. Heading for closure we here explore topological constraints. Results are straightforwardly obtained for averaged 2+1 model universes. For the relevant 3+1 case, we employ a method based on the Gauss-Bonnet-Chern theorem generalized to Lorentzian spacetimes and implement a sandwich approach to obtain spatial average properties. The 3+1 topological approach supplies us with a new equation linking evolution of scalar invariants of the expansion tensor to the norm of the Weyl tensor. From this we derive general evolution equations for averaged scalar curvature and kinematical backreaction, and we discuss related evolution equations on this level of the hierarchy of averaged equations. We also discuss the relation between topological properties of cosmological manifolds and dynamical topology change, e.g. as resulting from the formation of black holes.
In this paper we analyze the Dark Matter problem and the distribution of matter through two different approaches, which are linked by the possibility that the solution of these astronomical puzzles should be sought in the quantum imprinting of the Universe. The first approach is based on a cosmological model formulated and developed in the last ten years by the first and third authors of this paper; the so-called Archaic Universe. The second approach was formulated by Rosen in 1933 by considering the Friedmann-Einstein equations as a simple one-dimensional dynamical system reducing the cosmological equations in terms of a Schroedinger equation. As an example, the quantum memory in cosmological dynamics could explain the apparently periodic structures of the Universe while Archaic Universe shows how the quantum phase concernts not only an ancient era of the Universe, but quantum facets permeating the entire Universe today.
We analyze the semiclassical and quantum behavior of the Bianchi IX Universe in the Polymer Quantum Mechanics framework, applied to the isotropic Misner variable, linked to the space volume of the model. The study is performed both in the Hamiltonian and field equations approaches, leading to the surprising result of a still singular and chaotic cosmology, whose Poincare return map asymptotically overlaps the standard Belinskii-Khalatnikov-Lifshitz one. In the quantum sector, we reproduce the original analysis due to Misner, within the revised Polymer approach and we arrive to demonstrate that the quantum numbers of the point-Universe still remain constants of motion. This issue confirms the possibility to have quasi-classical states up to the initial singularity. The present study clearly demonstrates that the asymptotic behavior of the Bianchi IX Universe towards the singularity is not significantly affected by the Polymer reformulation of the spatial volume dynamics both on a pure quantum and a semiclassical level.
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.
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