Minisuperspace Cosmological Model Research Articles

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in [1]. In this paper, we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.

Noether symmetries and duality transformations in cosmology

We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans–Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans–Dicke parameter and it is a scale-factor duality when [Formula: see text]. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.

Two-oscillator Kantowski–Sachs model of the Schwarzschild black hole interior

In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model will be presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler-DeWitt equation and its general solutions, i.e. a wave function of the model, will be written, and then an adelic wave function will be constructed. Finally, thermodynamics of the model will be studied by using the Feynman-Hibbs procedure.

Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology

The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense) Lagrangian. We have used this method for the Regge-Teitelboim (RT) minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.

A late time accelerated FRW model with scalar and vector fields via Noether symmetry

We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann–Robertson–Walker (FRW) model, a scalar field with potential function V(ϕ) with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(ϕ). Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.

Noether symmetric classical and quantum scalar field cosmology

We study the evolution of a two-dimensional minisuperspace cosmological model in classical and quantum levels by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a Friedmann–Robertson–Walker model and a scalar field with which the action of the model is augmented. It is shown that the minisuperspace of such a model is a two-dimensional manifold with a vanishing Ricci scalar. We present a coordinate transformation which cast the corresponding minisupermetric to a Minkowskian or Euclidean one according to the choices of an ordinary or phantom model for the scalar field. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of the scalar field potential functions for which such symmetries exist. For these potential functions, the exact classical and quantum solutions in the cases where the scalar field is an ordinary or a phantom one are presented and compared.

Deformed phase space in a two-dimensional minisuperspace model

We study the effects of noncommutativity and deformed Heisenberg algebra on the evolution of a two-dimensional minisuperspace cosmological model in classical and quantum regimes. The phase-space variables turn out to correspond to the scale factor of a flat FRW model with a positive cosmological constant and a dilatonic field with which the action of the model is augmented. The exact classical and quantum solutions in commutative and noncommutative cases are presented. We also obtain some approximate analytical solutions for the corresponding classical and quantum cosmology in the presence of the deformed Heisenberg relations between the phase-space variables, in the limit where the minisuperspace variables are small. These results are compared with the standard commutative and noncommutative cases, and similarities and differences of these solutions are discussed.

Time asymmetries in quantum cosmology and the search for boundary conditions to the Wheeler–DeWitt equation

This paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since general relativity does not have a privileged time variable of Newtonian type, it is necessary, in order to have a dynamical evolution, to select a physical clock. This choice yields, in the proposed approach, to the breaking of the so-called clock-reversal invariance of the theory which is clearly distinguished from the well-known motion-reversal invariance of both classical and quantum mechanics. In light of this new perspective, the problem of imposing proper boundary conditions on the space of solutions of the Wheeler–DeWitt equation is reformulated. The symmetry-breaking formalism of previous papers is analyzed and a clarification of it is proposed in order to satisfy the requirements of the new interpretation.

P-Adic quantum cosmology

p-Adic quantum cosmology is one of the considerable applications of p-adic quantum theory, which takes into account possible nonarchimedean (ultrametric) aspects of space-time. For this reason, we consider minisuperspace cosmological models in the framework of p-adic and adelic quantum mechanics. In particular, we investigate the de Sitter model and obtain p-adic and adelic wave functions, which are briefly discussed.

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.

Simplest Cosmological Model with the Scalar Field

We investigate the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity. The classification of trajectories in closed minisuperspace Friedmann–Robertson–Walker model is presented. The possible fractal nature of a set of infinitely bounced trajectories is discussed. The results of numerical calculations are compared with those obtained by perturbative analytical calculations around the exactly solvable minisuperspace cosmological model with massless scalar field.

NONMINIMAL COUPLING AND QUANTUM COSMOLOGY

We consider a minisuperspace cosmological model generated by coupling nonminimally a vector field with the gravitational field. The classical solutions are divided into three sets: singular solutions, eternal universes with an expansion phase and flat spacetime. We apply quantum cosmological arguments to investigate which of them is the most probable classical solution. The semiclassical cosmological wave functions satisfy the correspondence principle, and examples are shown in which the three sets of classical solutions can be predicted from different classes of WKB wave functions. As a particular example we have considered the no-boundary wave function, which predicts flat spacetime. No solutions can be obtained from the tunneling boundary condition.

Quantum cosmological entropy production and the asymmetry of thermodynamic time.

The Hamiltonian for the time-dependent Schr\"odinger equation for matter fields derived from the Wheeler-DeWitt equation for a quantum minisuperspace cosmological model minimally coupled to free massive minimal scalar fields consists of a set of parameter-dependent and implicitly cosmological time-dependent harmonic oscillators. By using the generalized invariant method we obtain the exact quantum states whose number states at an earlier gravitational configuration in an expanding stage get evolved unitarily by a squeeze operator into the same number states at the later identical gravitational configuration in the subsequent recollapsing stage. It is proposed that during an expansion and the subsequent recollapse of the Universe following a wide class of wave functions of the quantum minisuperspace cosmological model, the cosmological entropy production determined by the squeeze parameters may break the symmetry of the thermodynamic time.

Conformally invariant cosmology based on Riemann-Cartan spacetime

A conformally invariant field-theoretical model including gravity based on the Riemann-Cartan spacetime U4 is considered. The cosmological scenario that follows from this model is discussed and a standard quantum gravitational formalism in the Arnowitt-Deser-Misner form is developed. The general formalism is then illustrated using the Bianchi-IX minisuperspace cosmological model. Wavefunctions of the universe in the de Sitter minisuperspace model with Vilenkin and Hartle-Hawking boundary conditions are considered and corresponding probability distributions for the scalar field values are calculated.

Geometric origin of cosmological time asymmetry in quantum cosmology

In the nonadiabatic path integral approach to a quantum minisuperspace cosmological model for the gravity minimally coupled to a matter field, the matter field gives rise to both a back reaction of the matter field Hamiltonian and a mode-dependent induced gauge potential (Berry's connection) to the separated gravitational field path integral. It is proposed that the mode-dependent gauge potential and the corresponding geometric phase for a closed loop of classical trajectory of the expanding and subsequently recontracting universe in the projected minisuperspace may break the symmetry of the cosmological time defined along the classical trajectory of the wave function of the universe.

Fermion sectors of supersymmetric diagonal Bianchi type ix cosmology

The mini-superspace cosmological model of Bianchi type IX with spatially homogeneous diagonal 3-metric and a cosmological term is extended to a spatially homogeneous supersymmetric model where an anti-commuting complex variable is added for each degree of freedom of the space-time metric and the cosmological term. Quantizing, a square root of the Wheeler DeWitt equation is obtained, which decouples in sectors of different fermion number. These fermion sectors are examined se[arately.

The phase structure in minisuperspace cosmological models

A phase space (PS) structure in minisuperspace cosmological models with gauge fields is investigated. It is shown for the SO( n ), n >3, gauge group that the physical PS differs from an ordinary plane. Due to this phenomenon, the path integral representation gets modified for the ground-state wave function of the Universe. It is also argued that the wormhole size quantization should change due to a non-trivial physical PS structure of gauge fields.

Canonical quantum Kaluza-Klein theory

We generalize some considerations concerning the gravitational canonical theory to a five-dimensional Kaluza-Klein theory. The quantization procedure is illustrated with a minisuperspace cosmological model. The results of the model indicate that a universe resembling our own and with an extra dimension has an oscillatory exponentially damped amplitude when the radius is vanishing.

Numerical calculations of minisuperspace cosmological models

The wave function of the universe is calculated numerically by solving the zero energy Schrödinger equation for homogeneous isotropic cosmological models with a massive scalar field or with curvature squared corrections to the action. The boundary condition used to integrate the equation is that the wave function should be given by a path integral over compact metrics.