Iso-Spectral Potentials and Inflationary Quantum Cosmology

Using the factorization approach of quantum mechanics, we obtain a family of isospectral scalar potentials for power law inflationary cosmology. The construction is based on a scattering Wheeler-DeWitt solution. These iso-potentials have new features, they give a mechanism to end inflation, as well as the possibility to have new inflationary epochs. The procedure can be extended to other cosmological models. PACS numbers: 02.30.Jr; 04.60.Ds; 04.60.Kz; 98.80.Cq.     

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studied.     

Quantum Cosmological Perfect Fluid Models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p = are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for < 1. Accelerated expansion at present requires –1/3 > > – 1.     

The Quantum Commutator Algebra of a Perfect Fluid

A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum operator in the denominator of some coordinate quantum commutators. It is shown that it is possible to multiply throughout by this momentum operator. Factor ordering differences can result in a viscosity term. The resulting quantum commutator algebra is unusual.     

Nonequilibrium Dynamics of Quantum Fields in Inflationary Cosmology

We summarize a recent study (with B. L. Hu) ofthe nonequilibrium dynamics of an unbroken-symmetryinflaton field during postinflationary reheating, duringwhich the energy density contained in the expectation value of the inflaton field is rapidlytransferred to inhomogeneous quantum modes of theinflaton field. The coupled dynamics of the expectationvalue (mean field) of a scalar inflaton field with anunbroken global O(N) symmetry and its quantum varianceis studied using the leading-order, large-Napproximation in a spatially flatFriedmann–Robertson–Walker (FRW) backgroundspacetime. The initial conditions for the mean field, variance, and Hubbleparameter were chosen to be consistent with conditionsat the end of slow roll in chaotic inflation.Backreaction of the dynamics of the mean field on thespacetime is incorporated self-consistently using thesemiclassical Einstein equation. The coupled dynamicalequations for the mean field, variance, and scale factorare solved for various choices of the mean field amplitude at the end of the slow-roll period,in order to determine the effect of spacetime curvatureon preheating, the parametricresonance-induced, rapid transfer of energy from themean field to the inhomogeneous inflaton modes. Itis shown that cosmic expansion can dramatically effectthe efficiency of preheating in the particular modelstudied.     

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.     

Integrable Multicomponent Perfect Fluid Multidimensional Cosmology II: Scalar Fields

We consider anisotropic cosmological models with a universe of dimension 4 or higher, factorized into n 2 Ricci-flat spaces, containing an m-component perfect fluid of m non-interacting homogeneous minimally coupled scalar fields under special conditions. We describe the dynamics of the universe: It has a Kasner-like behaviour near the singularity and isotropizes during the expansion to infinity. Some of the models considered are integrable, and classical as well as quantum solutions are found. Some solutions produce inflation from nothing. There exist classical asymptotically anti-de Sitter wormholes, and quantum wormholes with discrete spectrum.     

Toda Chains with Type Am Lie Algebra for Multidimensional m-component Perfect Fluid Cosmology

We consider a D-dimensional cosmological modeldescribing an evolution of Ricci-flat factor spaces,M₁,..., M_n (n 3), in thepresence of an m-component perfect fluid source (n– 1 m 2). We find characteristicvectors, related to the matter constants in thebarotropic equations of state for fluid components ofall factor spaces. We show that, in the case where wecan interpret these vectors as the root vectorsof a Lie algebra of Cartan type A _m = sl(m + 1, i), the model reduces tothe classical open m-body Toda chain. Using an eleganttechnique by Anderson for solving this system, weintegrate the Einstein equationsfor the model and present the metric in aKasner-like form.     

Quantum Cosmology with Hyperbolic Potential

For an FRW model with a minimally coupled scalar field having hyperbolic(exponential) potential we evaluate the wave function both by solving theWheeler-Dewitt (WD) equation and by evaluating the path integral. The WDequation is solved in configuration as well as in momentum space, while thepath integral is evaluated by dividing the lapse integral into a number of pieces.     

An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains

The quantum evolution equation of Loop Quantum Cosmology (LQC)—the quantum Hamiltonian constraint—is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schrödinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.     

Dynamical Vacuum in Quantum Cosmology

By regarding the vacuum as a perfect fluid with equation of state p = -, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.     

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.     

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.     

On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.     

Quantum Cosmology with Scalar-Vector and Scalar-Spinor Interactions

The problem of matter creation in the early Universe is considered in terms of quantum cosmology, introducing interactions of the scalar field with the spinor and vector fields of matter.     

Inflationary Cosmology with Two-component Fluid and Thermodynamics

We present a simple and self-consistent cosmology with a phenomenological model of quantum creation of radiation and matter due to the decay of the cosmological constant . The decay drives a non-isentropic inflationary epoch, which exits smoothly to the radiation-dominated era, without reheating, and then evolves to the dust era. The initial vacuum for radiation and matter is a regular Minkowski vacuum. The created radiation and matter obeys standard thermodynamic laws, and the total entropy produced is consistent with the accepted value. This paper is an extension of the model with the decaying cosmological constant considered in [1]. We compare our model with the quantum field theory approach to creation of particles in curved space.     

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.     

On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics

In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung [44], have been extensively used in Physics to investigate Superfluidity and Superconductivity phenomena [19,38] and more recently in the modeling of semiconductor devices [20] . Our approach is based on various tools, namely the wave functions polar decomposition, the construction of approximate solution via a fractional steps method which iterates a Schrödinger Madelung picture with a suitable wave function updating mechanism. Therefore several a priori bounds of energy, dispersive and local smoothing type, allow us to prove the compactness of the approximating sequences. No uniqueness result is provided.     

A Phase Transition in a Quantum Crystal with Asymmetric Potentials

A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided d ≥ 3, and the particle mass as well as the interaction intensity are big enough. The proof is based on the representation of local Gibbs states in terms of path measures and thereby on the use of the infrared estimates and the Garsia–Rodemich–Rumsey inequality.