Quantum Cosmological Solutions Research Articles

Classical and Quantum Cosmological Solutions in Teleparallel Dark Energy with Anisotropic Background Geometry

We investigate exact and analytic solutions for the field equations in the teleparallel dark energy model, where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exists for the description of the field equations, and variational symmetries are applied for the construction of invariant functions and conservation laws. The latter are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantum limit.

Quantum Cosmology with Many Fluids and the Choice of Cosmological Time

In this work we propose the quantization of a cosmological model describing the primordial universe filled with five barotropic fluids, namely: radiation, dust, vacuum, cosmic strings and domain walls. We intend to identify which fluid is best suited to provide phenomenologically the temporal variable in accordance with the observable universe. Through the Galerkin spectral method and the finite difference method in the Crank-Nicolson scheme (vacuum case), the quantum cosmological solutions are obtained and compared. We, also, compare the quantum cosmological solutions with the corresponding classical ones. The vacuum case is especially interesting because it provides a tunneling transition mechanism from the quantum to the classical phase and the possibility of calculating quantum tunneling probabilities.

Classical and quantum cosmological solutions in Bianchi type-I metric with fermionic field and relativistic fluid in Schutz’s formalism

A model for an anisotropic pre-inflationary universe described by the Bianchi type-I metric is developed. A relativistic fluid of the Schutz formalism and a self-interacting fermionic field are considered as sources of the gravitational field. The classical analysis is based on the Hamiltonian formalism written in terms of the Misner variables and it is shown that the fluid degrees of freedom can be embodied by a conformal time variable. The three classical scale factors are obtained as functions of the conformal time. The quantum analysis follows from the de Broglie–Bohm formalism applied to the wave function which is a solution of the Wheeler–DeWitt equation and the three scale factors are also determined as functions of the conformal time. While the classical expressions for the scale factors show a singularity when the conformal time vanishes, their quantum expressions exhibit bouncing behavior. It is possible to adjust the behavior of the classical and quantum scale factors as functions of the conformal time so that they have a common isotropic behavior at late times with a dilution of the quantum effects.

SIGNS AND COSMOLOGY

Using a new effective action predicted from quantum gravity where the sign of the Euclidean Einstein action is reversed, we discuss Wentzel–Kramers–Brillouin (WKB) solutions in quantum cosmology and predict that this sign change might explain the origin of phantom scalars.

Classical and quantum cosmology of multigravity

Recently, a multigraviton theory on a simple closed circuit graph corresponding to the discretization of S1 compactification of the Kaluza–Klein (KK) theory has been considered. In the present paper, we extend this theory to that on a general graph and study what modes of particles are included. Furthermore, we generalize it in a possible nonlinear theory based on the vierbein formalism and study classical and quantum cosmological solutions in the theory. We found that scale factors in a solution for this theory repeat acceleration and deceleration.

A tale of two symmetries or the quantum universe from supersymmetry and duality

Research on the very early Universe has gradually been benefiting from the recent emergence of two attractive lines of investigation: Supersymmetric Quantum Cosmology and String inspired Quantum Cosmology. The essential feature is that supersymmetry is explicitly present in the former, while the presence of duality properties is characteristic of the latter. Moreover, it seems that quantum cosmological solutions can be assigned with “hidden” supersymmetric properties, whose origin can be traced to a duality present in the classical string action. In this brief review we will therefore analyse some of the consequences of explicitly including supersymmetry and/or duality properties in a quantum cosmological scenario. In addition, several open issues in quantum cosmology are also introduced.

Ψ=We ±Φ Quantum cosmological solutions for class A Bianchi models

We find solutions for quantum Class A Bianchi models of the form $\rm \Psi=W e^{\pm \Phi}$ generalizing the results obtained by Moncrief and Ryan in standard quantum cosmology. For the II and IX Bianchi models there are other solutions $\rm \tilde\Phi_2$, $\rm \tilde\Phi_9$ to the Hamilton-Jacobi equation for which $\rm \Psi$ is necessarely zero, in contrast with solutions found in supersymmetric quantum cosmology.

Wave function with second order correction and inflationary solutions in quantum cosmology

A brief account for the higher order wave function in Hartle-Hawking (H-H) proposal is given which is compared with the tunneling wave function due to Vilenkin. The probability distributions are determined for both types of wave functions. Also a class of solutions are evaluated using H-H approach for Kantowski-Sachs metric with a scalar field and inflation is observed.

Inflationary solutions in quantum cosmology

The authors prove that in the Hartle-Hawking approach to quantum cosmology the existence of an inflationary phase is a general property of minisuperspace models given by a closed Friedmann-Robertson-Walker universe containing a massless scalar field with a lambda phi n self-interaction. The evolution in time of the cosmic scale factor and of the scalar field in the very early universe is derived, together with the constraints to be satisfied in order to solve the horizon and flatness problems.