Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology

First a Friedmann-Robertson-Walker (FRW)universe filled with dust and a conformally invariantscalar field is quantized. For the closed model we finda discrete set of wormhole quantum states. In the case of flat spacelike sections we find states withclassical behaviour at small values of the scale factorand quantum behaviour for large values of the scalefactor. Next we study a FRW model with a conformally invariant scalar field and a nonvanishingcosmological constant dynamically introduced byregarding the vacuum as a perfect fluid with equation ofstate p = –. The ensuing Wheeler-DeWittequation turns out to be a bona fide Schrodinger equation, andwe find that there are realizable states with a definitevalue of the cosmological constant. Once again we findfinite-norm solutions to the Wheeler-DeWitt equation with definite values of thecosmological constant that represent wormholes,suggesting that in quantum cosmological models with asimple matter content wormhole states are a commonoccurrence.     

Creation of Unstable Particles and Decoherence in Semiclassical Cosmology

We consider a simple cosmological model in orderto show the importance of unstable particle creation forthe validity of the semiclassical approximation. Usingthe mathematical structure of rigged Hilbert spaces we show that particle creation is theseed of decoherence which enables the quantum toclassical transition.     

The Relation of Generalized Scalar-Tensor Theory with the 5D Space-Time-Matter Theory

The relationship between cosmological solutionsof five-dimensional Space-Time-Matter (STM) theory anda Generalized Scalar-Tensor (GST) theory is investigatedin which the cosmological term Lambda depends not only on a scalar field but also onits time derivative .Identification of these solutions allows us to solve forthe functional form of the cosmological term, and mayhave relevance for the early Universe.     

Nonminimal Derivative Coupling and the Recovering of Cosmological Constant

We show that the existence of the cosmologicalconstant can be connected to a nonminimal derivativecoupling, in the action of gravity, between the geometryand the kinetic part of a given scalar fieldwithout introducing any effective potential ofscalar fields. Exact solutions are given.     

Spherically Symmetric Space-Time with Two Cosmological Constants

We present the analytic spherically symmetric solution of the Einstein equations, which has de Sitter asymptotics for both r and r 0. This two-lambda spherically symmetric solution is globally regular. At the range of mass parameter M_cr1 < M < M_cr2 it has three horizons and describes a neutral black hole whose singularity is replaced by a cosmological constant of Planck or GUT scale, at the background of small . Global structure of space-time contains an infinite sequence of black and white holes, de Sitter-like past and future regular cores (with + at r 0) replacing singularities, asymptotically de Sitter external universes (with for r ), and spacelike infinities. In the range of mass parameter M < M_cr1 we have a one-horizon solution describing recovered selfgravitating particle-like structure at the background of small , and for M > M_cr2 another one-horizon configuration which can be called de Sitter bag. The solutions with M = M_cr1 and M = M_cr2 represent two extreme states of a neutral nonsingular cosmological black hole.     

Cosmological Models with Bulk Viscosity in the Presence of Particle Creation

The effect of bulk viscosity, with a time varying bulk viscous coefficient, on the evolution of frw models is investigated in the context of open thermodynamic systems, which allows for particle creation. It is seen that, by choosing an appropriate function for particle creation, the models presented exhibit non-singular beginnings.     

Evolution of Thin-wall Configurations ofTexture Matter

We consider the matter of global textures withinthe frameworks of a perfect fluid model in generalrelativity. We examine thermodynamical properties oftexture matter in comparison with radiation fluid and bubble matter. Then we study dynamics ofthin-wall selfgravitating texture objects, and show thatclassical motion can be elliptical (finite), parabolicalor hyperbolical. It is shown that total gravitational mass of neutral textures in equilibrium equalszero, as was expected. Finally, we carry out theWheeler-DeWitt minisuperspace quantization of thetheory, obtain exact wave functions and discrete spectra of bound states with provision for spatialtopology.     

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.     

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.     

Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions

In the framework of Bianchi I (BI) cosmological models a self-consistent system of interacting spinor and scalar fields has been considered. We introduced an interaction function F(I, J) which is an arbitrary function of invariants I and J, generated from the real bilinear forms of the spinor field. Exact self-consistent solutions to the field equations have been obtained for the cosmological model filled with perfect fluid. The initial and the asymptotic behavior of the field functions and of the metric one has been thoroughly studied.     

Bianchi A Cosmological Models as the Simplest Dynamical Systems in R4

The behaviour of the vacuum non-tilted Bianchimodels of class A is studied in terms of dynamicalsystems theory. We introduce phase variables in whichthe Hamiltonian constraint is solved algebraically. It is shown that in these variables BianchiVIII and Bianchi IX models assume the form of afour-dimensional autonomous system with a polynomialvector field defined on the phase space, whereas Bianchi I and Bianchi II world models can be presentedas a one- and two-dimensional system, respectively. TheBianchi VI₀ and Bianchi VII₀ worldmodels are represented as a three-dimensional dynamicalsystem.     

Inheriting Conformal and Special Conformal Killing Vectors in String Cosmology

In this paper we study the consequences of the existence of conformal and special conformal Killing vectors (CKV, SCKV) for string cloud and string fluid in the context of general relativity. The inheritance symmetries of the string cloud and string fluid are discussed. Einstein's field equations have been solved for static spherically symmetric space-time with cloud and fluid of strings source via CKV.     

Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is shown that there often exists a particular set of solutions to the field equations of pure gravity theories, consisting of different combinations of curvature tensors, which satisfies the vacuum equations with cosmological constant. Implications of generalized symmetries of the field equations derived from the superstring effective action for the cosmological constant problem are discussed.     

Higher-derivative Quantum Cosmology

The quantum cosmology of a higher-derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler–DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler–DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.     

Dynamical Study of a Constant Viscous Dark Energy Model in Classical and Loop Quantum Cosmology

Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology.Assuming that the dark energy has a constant bulk viscosity,it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of deSitter type,whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed.Moreover,our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.     

Quantum Cosmology in CGBD Theory

We apply the theory developed in quantum cosmology to a model of charged generalized Brans–Dicke gravity. This is a quantum model of gravitation interacting with a charged Brans–Dicke type scalar field which is considered in the Pauli frame. The Wheeler–DeWitt equation describing the evolution of the quantum Universe is solved in the semiclassical approximation by applying the WKB approximation. The wave function of the Universe is also obtained by applying both the Vilenkin-like and the Hartle–Hawking-like boundary conditions. We then make predictions from the wave functions and infer that the Vilenkin's boundary condition is more reasonable in the Brans–Dicke gravity models leading a large vacuum energy density at the beginning of the inflation.     

Neutrinos in a Vacuum Dominated Cosmology

We explore the dynamics of neutrinos in a vacuum dominated cosmology. First we show that such a geometry will induce a phase change in the eigenstates of a massive neutrino and we calculate the phase change. We also calculate the delay in the neutrino flight times in this geometry. Applying our results to the presently observed background vacuum energy density, we find that for neutrino sources further than 1.5 Gpc away both effects become non-trivial, being of the order of the standard relativistic corrections. Such sources are within the observable Hubble Deep Field. The results which are theoretically interesting are also potentially useful, in the future, as detection techniques improve. For example such effects on neutrinos from distant sources like supernovae could be used, in an independent method alternative to standard candles, to constrain the dark energy density and the deceleration parameter. The discussion is extended to investigate Caianiello's inertial or maximal acceleration (MA) effects of such a vacuum dominated spacetime on neutrino oscillations. Assuming that the MA phenomenon exists, we find that its form as generated by the presently observed vacuum energy density would still have little or no measurable effect on neutrino phase evolution, for neutrinos in the energy range of a few eV.     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

The Structure of the Extreme Schwarzschild-de Sitter Space-time

The extreme Schwarzschild-de Sitter space-timeis a spherically symmetric solution of Einstein'sequations with a cosmological constant Lambda and massparameter m > 0 which is characterized by thecondition that 9m² = 1. The globalstructure of this space-time is here analyzed in detail.Conformal and embedding diagrams are constructed, andsynchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture arepresented. The permitted geodesic motions are alsoanalyzed. By a careful investigation of the geodesicsand the equations of geodesic deviation, it is shown that specific families of observers escape fromfalling into the singularity and approach nonsingularasymptotic regions which are represented by specialpoints in the complete conformal diagram.The redshift of signals emitted by particles whichfall into the singularity, as detected by those observers which escape, is also calculated.     

Selection Rules in Minisuperspace Quantum Cosmology

The existence of a Noether symmetry for a given minisuperspace cosmological model is a sort of selection rule to recover classical behaviours in cosmic evolution since oscillatory regimes for the wave function of the universe come out. The so-called Hartle criterion to select correlated regions in the configuration space of dynamical variables can be directly connected to the presence of a Noether symmetry and we show that such a statement works for generic extended theories of gravity in the framework of minisuperspace approximation. Examples and exact cosmological solutions are given for nonminimally coupled and higher-order theories.