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Register a new userThe Time Evolution of Quantum Universe in The Quantum Potential Picture
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Authors
A.Blaut & J. Kowalski-Glikman
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We use the quantum potential approach to analyse the quantum cosmological model of the universe. The quantum potential arises from exact solutions of the full Wheeler-De Witt equation.
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We study the time evolution of a wave function for the spatially flat Friedmann-Lemaitre-Robertson-Walker universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchar dust as a matter field in order to introduce a clock in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the universe obeys the classical time evolution in the late time but its variance diverges.
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.
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.
We derive the primordial power spectra and spectral indexes of the density fluctuations and gravitational waves in the framework of loop quantum cosmology (LQC) with holonomy and inverse-volume corrections, by using the uniform asymptotic approximation method to its third-order, at which the upper error bounds are $lesssim 0.15%$, and accurate enough for the current and forthcoming cosmological observations. Then, using the Planck, BAO and SN data we obtain the tightest constraints on quantum gravitational effects from LQC corrections, and find that such effects could be well within the detection of the current and forthcoming cosmological observations.
Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energys level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p,c^2$, and a B-H temperature: $T_{BH}=left(frac{hbar,c}{2pi,l_p,K_B}right)$.
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