D = 1 Supergravity and Quantum Cosmology

Using a D = 1 supergravity framework I construct a super-Friedmann equation for an isotropic and homogenous universe including dynamical scalar fields. In the context of quantum theory this becomes an equation for a wave function of the universe of spinorial type, the Wheeler–DeWitt–Dirac equation. It is argued that a cosmological constant breaks a certain chiral symmetry of this equation, a symmetry in the Hilbert space of universe states, which could protect a small cosmological constant from being affected by large quantum corrections.

     

Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler–DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler–DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.     

Quantum cosmology in 2+1 and 3+1 dimensions

We study the Wheeler-DeWitt equations for the wave function of the universe in 2+1 and 3+1 dimensions. Perturbation methods are developed and the first few orders areexplicitly calculated for the case of an inflating universe. We find that early quantum fluctuation can produce large-scale inhomogenities in the global structure of the universe at later times.     

Quintom Potentials from Quantum Cosmology Using the FRW Cosmological Model

We construct the quintom potential of dark energy models in the framework of spatially flat Friedmann–Robertson Walker universe in the inflationary epoch, using the Bohm like approach, known as amplitude-real-phase. We find some potentials for which the wave function of the universe is found analytically and we have obtained the classical trajectories in the inflation era.     

WAVE FUNCTIOM OF THE UNIVERSE WITH QUAETUM CORRECTION OF MATTER FIELDS

Considering the effective gravitational actionincluding the quantum correction of the matter fields, we calculate nearly realistic wave function of the universe by using the scheme of Hartle and Hawking. The particular case with the cosmological constant Λ=0 is discussed, then the conclusion that the spacetime may be de Sitter's without Λ is obtained, this is just a result of interaction between gravity and matter fields. When the radius of the universe is larger than 10^-1lp, the universe must be on the classical epoch. This paper shows that a practical quantum model of the universe is possible.     

Massless Spin–Zero Particle and the Classical Action via Hamilton–Jacobi Equation in G?del Universe

In this letter we investigate the separability of the Klein–Gordon and Hamilton–Jacobi equation in G?del universe. We show that the Klein–Gordon eigen modes are quantized and the complete spectrum of the particle’s energy is a mixture of an azimuthal quantum number, m and a principal quantum number, n and a continuous wave number k. We also show that the Hamilton–Jacobi equation gives a closed function for classical action. These results may be used to calculate the Casimir vacuum energy in G?del universe.     

Classical and quantum Hořava–Lifshitz cosmology in a minisuperspace perspective

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity theory proposed by Ho?ava, the so-called Ho?ava–Lifshitz theory of gravity. Beginning with the ADM representation of the action corresponding to this model, we construct the Lagrangian in terms of the minisuperspace variables and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Ho?ava theory. Either in the matter free or in the case when the considered universe is filled with a perfect fluid, the exact solutions to the classical field equations are obtained for the flat, closed and open FRW model and some discussions about their possible singularities are presented. We then deal with the quantization of the model in the context of the Wheeler–DeWitt approach of quantum cosmology to find the cosmological wave function. We use the resulting wave functions to investigate the possibility of the avoidance of classical singularities due to quantum effects.     

Klein–Gordon and Dirac Equations in de Sitter Space–Time

We present and discuss the Klein–Gordonand Dirac wave equations in the de Sitter universe. Toobtain the Dirac wave equation we use the factorizationof the second-order invariant Casimir operatorassociated to the Fantappie–de Sitter group. Boththe Klein–Gordon and Dirac wave equations arediscussed in terms of the spherical harmonics with spinweight. A particular case of Dirac wave equation issolved in terms of a new class of polynomials.     

Modeling the quantum evolution of the universe through classical matter

It is well known that the canonical quantization of the Friedmann–Lemaître–Robertson–Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $\left<a\right>(t)$ never vanishes and, as $t\rightarrow \infty $ , we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.     

Traversable braneworld wormholes supported by astrophysical observations

In this study, we investigate the characteristics and properties of a traversable wormhole constrained by the current astrophysical observations in the framework of modified theories of gravity (MOG). As a concrete case, we study traversable wormhole space–time configurations in the Dvali–Gabadadze–Porrati (DGP) braneworld scenario, which are supported by the effects of the gravity leakage of extra dimensions. We find that the wormhole space–time structure will open in terms of the 2σ confidence level when we utilize the joint constraints supernovae (SNe) Ia + observational Hubble parameter data (OHD) + Planck + gravitational wave (GW) and z < 0:2874. Furthermore, we obtain several model-independent conclusions, such as (i) the exotic matter threading the wormholes can be divided into four classes during the evolutionary processes of the universe based on various energy conditions; (ii) we can offer a strict restriction to the local wormhole space–time structure by using the current astrophysical observations; and (iii) we can clearly identify a physical gravitational resource for the wormholes supported by astrophysical observations, namely the dark energy components of the universe or equivalent space–time curvature effects from MOG. Moreover, we find that the strong energy condition is always violated at low redshifts.     

High energy description of dark energy in an approximate 3-brane Brans–Dicke cosmology

We consider a Brans–Dicke cosmology in five-dimensional space–time. Neglecting the quadratic and the mixed Brans–Dicke terms in the Einstein equation, we derive a modified wave equation of the Brans–Dicke field. We show that, at high energy limit, the 3-brane Brans–Dicke cosmology could be described as the standard one by changing the equation of state. Finally as an illustration of the purpose, we show that the dark energy component of the universe agrees with the observations data.     

Cosmological perturbations and quantum fields in curved space

We identify the quantum theory of cosmological perturbations with the quantum field theory in curved spacetime with emphasis on its field concept. We materialize this idea by using a coherent state as a quantum analogue of a nontrivial classical field configuration. We present analytic results in a de Sitter universe for the massless and massive minimal free scalar fields. Some new features on the spectrum of perturbations are obtained for the massive case. We also show how such quantum field theories can be derived from quantum gravity using the semiclassical approximation. A physical degree of freedom is picked up from three scalar perturbations in the quantum gravity scalar system and its Schrödinger equation is derived. Peculiar features of quantum fields at imaginary time and its possible implications on boundary conditions for the wave function of the universe are also discussed.     

An approach to dark energy problem through linear invariants

The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that the coherent state is an eigenstate of an annihilation operator, the wave function.in the coherent state is easily evaluated by solving the eigenvalue equation of the linear invariants. The expectation value of the vacuum energy density is derived using this wave function.Fluctuations of the scalar field and its conjugate momentum are also investigated. Our theory based on the linear invariant shows that the vacuum energy density of the universe in a coherent state is decreased continuously with time due to nonconservative force acting on the coherent oscillations of the scalar field,which is provided by the expansion of the universe. In effect, our analysis reveals that the vacuum energy density decreases in proportion to t-β where β is 3/2 for radiation-dominated era and 2 for matter-dominated era. In the case where the duration term of radiation-dominated era is short enough to be negligible, the estimation of the relic vacuum energy density agrees well with the current observational data.     

Wave Functions for Arbitrary Operator Ordering in the de Sitter Minisuperspace Approximation

We derive exact series solutions for the Wheeler–DeWitt equation corresponding to a spatially closed Friedmann–Robertson–Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. The resulting wave functions are those relevant to the approximation which has been widely used in two-dimensional minisuperspace models with an inflationary scalar field for the purpose of predicting the period of inflation which results from competing boundary condition proposals for the wave function of the universe. The problem that Vilenkin's tunneling wave function is not normalizable for general operator orderings, is shown to persist for other values of the spatial curvature, and when additional matter degrees of freedom such as radiation are included.     

Why is the universe so large?

S. W. Hawking's proposal for the wave function of the universe, if correct, determines the conditional probabilities for all properties of the universe. In a simple minisuperspace model it predicts that at any given nonzero energy density, the universe is most probably infinitely large.     

充满物质的Friedmann-Robertson-Walker宇宙的稳定性

研究了在含有宇宙(学)常数的Friedmann-Robertson-Walker宇宙模型中,充满、满足p=(γ-1)ρ物质宇宙的稳定性.通过计算引力波的扰动,以及dp/dp=γ-1的扰动,得到对于ε=-1,Λ<0,满足Einstein场方程的宇宙只要γ≥0是不稳定的. 关键词： 充满物质的Friedmann-Robertson-Walker宇宙 虫洞 时空稳定性     

Loss of incoherence and determination of coupling constants in quantum gravity

The wave function of an interacting ‘family’ of one large ‘parent’ and many Planck-sized ‘baby’ universes is computed in a semiclassical approximation using an adaptation of Hartle-Hawking initial conditions. A recently discovered gravitational instanton which exists for general relativity coupled to axions is employed. The outcome of a single experiment in the parent universe is in general described by a mixed state, even if the initial state is pure. However, a sequence of measurements rapidly collapses the wave function of the family of universes into one of an infinite number of ‘coherent’ states for which quantum incoherence is not observed in the parent universe. This provides a concrete illustration of an unexpected phenomena whose existence has been argued for on quite general grounds by Coleman: quantum incoherence due to information loss to baby universes is not experimentally observable. We further argue that all coupling constants governing dynamics in the parent universe depend on the parameters describing the particular coherent state into which the family wave function collapses. In particular, generically terms that violate any global symmetries will be induced in the effective action for the parent universe. These last results have much broader applicability that our specific model.     

Cardy–Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

We derive a formula for the entropy for a multicomponent coupled fluid, which under special conditions reduces to the Cardy–Verlinde form relating the entropy of a closed FRW universe to its energy together with its Casimir energy. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and also modified gravity is included in terms of its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy–Verlinde formula corresponding to the 2d CFT entropy in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all known four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that, except from some special cases of Type II and Type IV singularities, the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter universe.     

Quantum-like Interpretation of Dirac Wave Equation in?Robertson-Walker Geometry

The Dirac wave equation is separated in the Robertson-Walker metric. The resulting radial equation is interpreted as a one dimensional quantum-like equation that is explicitly solved. There results that the energy spectrum, that is determined in the flat, open and closed universe, is independent of the mass of the particle. Moreover it is the same of the massless neutrino case previously studied. In the closed metric case the discrete positive spectrum is asymptotically determined. The separation of the energy levels is however very far from being experimentally tested.     

De Broglie-Bohm Interpretation of Canonical Quantum Cosmology Implies Early Stages of the Universe Dominated by Radiation

The Einstein's general relativity is formulated in the Hamiltonian form for a spatially flat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler-DeWitt equation. Solving the Wheeler-DeWitt equation and employing the de Broglie-Bohm interpretation to the wave function of the universe, we obtain a new version of spatially flat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufficiently small.