Origin of structure in the Universe (original) (raw)
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Wave function of the Universe in the early stage of its evolution
The European Physical Journal C, 2008
In quantum cosmological models, constructed in the framework of Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor a at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor a. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of modulus of wave function in the external region starting from the turning point which decrease with increasing of a and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing a and can be used as a fully quantum dynamical characteristic of the expansion of the Universe. Key words. quantum cosmology, Wheeler-De Witt equation, wave function of Universe, tunneling boundary conditions PACS. 98.80.Qc Quantum cosmology -98.80.k Cosmology -98.80.Bp Origin and formation of the Universe, Big Bang theory -98.80.Jk Mathematical and relativistic aspects of cosmology Send offprint requests to:
The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and A &0. The ground state corresponds to de Sitter space in the classical limit.
The Schrodinger picture of standard cosmology
2009
We consider a time independent Schrödinger type equation derived from the equations of motion that drives a single scalar field in a standard cosmology model for inflation in a flat space-time with a Friedman-Robertson-Walker (FRW) metric with a cosmological constant. We find that all the 1-dimensional bound state solutions of quantum mechanics lead to at least one exact solution for the dynamical equations of standard cosmology, and that these solutions resemble the most recurrent inflationary solutions found in the literature. The analogies derived from this approach may be used to realize a deeper understanding of the dynamics of the model.
Inflation in multidimensional quantum cosmology
Physical Review D, 1996
We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a D + 4-dimensional spacetime of topology R × S 3 × S D , with a field ("chaotic inflaton") for the matter component. Einstein compactification are assumed. The resulting minisuperspace is 3-dimensional. Wheeler-DeWitt and the probability compactifying extra dimensions. Our conclusion is that the most likely initial conditions, although they do not lead to the compactification of the internal space, still yield (power-law) inflation for the outer space. The scenario is physically acceptable because the inner space growth is limited to ∼ 10 11 in 100 e-foldings of inflation, starting from the Planck scale.
2004
In these notes I will review our present understanding of the origin and evolution of the universe, making emphasis on the most recent observations of the acceleration of the universe, the precise measurements of the microwave background anisotropies, and the formation of structure like galaxies and clusters of galaxies from tiny primodial fluctuations generated during inflation. 1
Origin of the large scale structures of the universe
Physical Review D, 2004
We revise the statistical properties of the primordial cosmological density anisotropies that, at the time of matter radiation equality, seeded the gravitational development of large scale structures in the, otherwise, homogeneous and isotropic Friedmann-Robertson-Walker flat universe. Our analysis shows that random fluctuations of the density field at the same instant of equality and with comoving wavelength shorter than the causal horizon at that time can naturally account, when globally constrained to conserve the total mass (energy) of the system, for the observed scale invariance of the anisotropies over cosmologically large comoving volumes. Statistical systems with similar features are generically known as glass-like or lattice-like. Obviously, these conclusions conflict with the widely accepted understanding of the primordial structures reported in the literature, which requires an epoch of inflationary cosmology to precede the standard expansion of the universe.
Revisiting the spectrum of a scalar field in an anisotropic universe
Journal of the Korean Physical Society, 2014
We revisit the issue on signatures of pre-inflationary background anisotropy by considering the quantization of a massless and minimally coupled scalar field in an axially symmetric Kasner background, mimicking cosmological perturbations. We show that the power spectrum of the scalar field fluctuation has a negligible difference from the standard inflation in the non-planar directions, but it has a sharp peak around the symmetry plane. For the non-planar high-momentum modes, we use the WKB approximation for the first period and the asymptotic approximation based on the de Sitter solution for the next period. At the boundary, two mode functions have the same accuracy with error of O(Hi/k). We calculate the approximation up to the order of (Hi/k) 6 and show that the power spectrum of the scalar field fails to get corrections until we execute the approximation up to 6 th order.
A New Vision of the Big Bang Cosmology
Universal Journal of Physics and Application, 2014
In this paper we show how the inhomogeneity in the matter distribution produced until the time of the last scattering surface in the light of some spatially homogeneous but anisotropic models, produced anisotropies that on large angular scales (larger than ϑ ∼ > 2 •) not differ from those considered in Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. For these anisotropic models the mark left in the cosmic microwave background radiation by fluctuations density primordial, in the form of a fractional variation of temperature of this radiation, is governed by the same expression which is used for FLRW models. More specifically, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, since the anisotropy of the global expansion is small at the time of the last scattering surface. This conclusion is in agreement with previous work on the same anisotropic models, where they undergo a process of 'isotropization' to the extent that the observations are unable to distinguish them from the FLRW models, if the Hubble parameters along the orthogonal directions are assumed approximately equal to the current present epoch. We considered upper bounds for the current values of the anisotropic parameters imposed by COBE observations.
Quantum Cosmology in the Unified Field
Quantum Cosmology in the Unified Field, 2023
Quantum Cosmology describes the nature of the universe from a perspective of an unobserved and largely unseen microcosm forming the basis for an experienced and observed macrocosm. It so presents a cosmogenesis, a description of the origins as an ontology for cosmological models. The building blocks of an experienced physical reality in atomic, molecular and subatomic constituents then emerge in models and paradigms of science from an observed and measured wave-particle duality which couples the microcosm of the quantum realm to its macrocosmic cooperator within a collectivized physical reality. Quantum Cosmology proposes the emergence of the quantum world manifesting in an experienced spacetime of energy interactions for a thermodynamically expanding universe to derive from a preexisting timespace forming the reason and purpose for the existence of a physical reality experienced in the world of the macrocosm. The relevant physics for the kaleidoscope and interplay of energy describing the universe modelled in the physics of a Planck-Einstein black body radiator then utilizes the emitted electromagnetic radiation spectrum to derive and apply the initial and boundary conditions for the cosmology manifesting in the experienced spacetime. Quantum Cosmology expands on the premises of Special and General Relativity for a description of spacetime in introducing the concept of Quantum Relativity (QR), emerging from the timespace to become the cornerstone for a Unified Field of Quantum Relativity (UFoQR). The Unified Field defines the parameters for the microcosmic reality experienced and observed in spacetime from the platform of the timespace in the emergence of space and time from an algorithmically defined energy matrix described in a multidimensional setting of mathematical logistical statements and principles. The birth of space in the formulation of an inflaton and the birth of time in the form of an instanton follow the self-generation of dimensions from a prior abstractly defined existence in timespace to become a multidimensional physicalized reality in the spacetime. The abstract nature of the timespace as originator for the spacetime is defined as a form of universalized consciousness and as a concept of being 'self-aware' of occupying the spacetime from a prior state of being unaware in the spacelessness and timelessness of the timespace. In particular the occupancy of spacetime volumars as the basis universalized consciousness is defined in Quantum Relativity as a spacial awareness in the form of a radius independent form of quantum spin-acceleration as the frequency over time differential df/dt defining an initializing maximized frequency permutation count. The square of frequency then forms a basis to couple maximized and minimized energy states, modelled on a multidimensional 12-dimensional cosmology described as a T-duality modular mirror duality. The nature of quantum gravitation, for example, then is described in gravitational waves using the squared frequency state (as G times density) to couple to the universalized consciousness quantization in the form of the gravitational parameter GM with mensuration units identical to the universal consciousness quantum as the magnetic charge of a Dirac monopole and as evidenced in the charge formulation of Newman-Kerr black hole s(r)ingularities (manifold singularity without thickness). The spacetime realism intersecting the timespace abstraction then becomes the multidimensional energy continuum for the wave-particle duality enabling the microcosm to self-replicate in holographic fractalization to evolve into an observable and measurable macrocosmic physical reality. This book is presented for the scientifically literate reader and researcher and can be said to follow a Newtonian tradition and to be inclusive of an holistic metaphysically overviewing cosmology.
1998
Abstract: We briefly present the supersymmetric double Darboux method and next apply it to the continuum of the quantum Taub cosmological model as a toy model in order to generate a one-parameter family of bosonic Taub potentials and the corresponding wavefunctions. Recently, extensive work has been devoted to generating quasi-isospectral potentials by the methods of supersymmetric quantum mechanics (SUSYQM) [1]. This work starts from the one dimensional (1D) Schrödinger equation with a given potential (called “bosonic ” potential V−), whose “ground-state ” (nodeless) wave function is known too. The method allows one to generate families of new potentials, which may look quite different form the original one, but have the same discrete spectrum up to the ground state. SUSYQM is in fact based on a procedure already known to Darboux [2]. We shall use an extension of SUSYQM formalism based on the general Riccati equation and on a state U0(x) of a potential V−(x), by which one can gener...