Nivaldo A. Lemos

Quantum Cosmological Perfect Fluid Models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p = αρ are constructed using Schutzs 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 α < 1. Accelerated expansion at present requires −1/3 > α > − 1.

Dynamical Vacuum in Quantum Cosmology

By regarding the vacuum as a perfect fluid with equation of state p = -ρ, de Sitters 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.

On the quantization of constrained generalized dynamics

A special class of degenerate second‐order Lagrangians, those that differ from a nondegenerate first‐order Lagrangian by a total time derivative (or a four‐divergence) of a function of both the coordinates and velocities, is studied in detail. Using Dirac’s theory of constrained systems, it is shown that the canonical quantization starting from the second‐order Lagrangian leads to the same physical results as those obtained from the nondegenerate first‐order Lagrangian. Then some incorrect results and misleading arguments encountered in the literature on the subject are clarified.

Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation

The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang-big crunch) at the quantum level. We show that a proper study of their model does not indicate that it prevents the occurrence of singularities at the quantum level, in fact the quantum probability of such event is larger than the classical one. Our numerical simulations based on the powerful variational sinc collocation method (VSCM) also show that the precision of the results of that paper is much lower than the 20 significant digits reported by the authors.

Canonical approach to the damped harmonic oscillator

We present a canonical treatment of the damped harmonic oscillator. The Hamiltonian is made simpler by means of a suitable canonical transformation. The ensuing equations of motion for the transformed canonical variables are then solved by the Hamilton‐Jacobi method.

Dissipative forces and the algebra of operators in stochastic quantum mechanics

Abstract Davidsons construction of a Hilbert space and of quantum operators on the basis of the Fenyes-Nelson stochastic mechanics is extended to the case in which a dissipative force linear in the velocity is present. The hamiltonian becomes a nonlinear operator but the position and linear momentum operators are the same as in ordinary quantum mechanics.

A Quantum Cosmological Model with Static and Dynamic Wormholes

Quantization is performed for a Friedmann-Robertson-Walker universe filled with a conformally invariant scalar field and a perfect fluid with equation of state p = α ρ. A well-known discrete set of static quantum wormholes is shown to exist for radiation (α = 1/3), and a novel continuous set is found for cosmic strings (α = −1/3), the latter states having throat radii of any size. In both cases wave-packet solutions to the Wheeler-DeWitt equation are obtained with all the properties of evolving quantum wormholes. In the case of a radiation fluid, a detailed analysis of the quantum dynamics is made in the context of the Bohm-de Broglie interpretation. It is shown that a repulsive quantum force inversely proportional to the cube of the scale factor prevents singularities in the quantum domain. For the states considered, there are no particle horizons either.

Can quantum gravitational effects influence the entire history of the Universe

In this work, a flat Friedmann-Robertson-Walker universe with dust and a cosmological constant is quantized. By means of a canonical transformation, the classical Hamiltonian is reduced to that of either a harmonic oscillator or anti-oscillator, depending on whether {lambda} 0, respectively. In this way, exact solutions to the Wheeler-DeWitt equation can easily be obtained. It turns out that a positive cosmological constant alone may account for an early inflationary regime and a later accelerated expansion phase, with a period of decelerated expansion in between. This suggests that quantum-gravitational effects can influence most of the history or even the entire history of the Universe.

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 = –ρ. 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.

Note on the Langrangian description of dissipative systems

Constraints are placed on the form of the Lagrangian for dissipative systems consistent with dH/dt = dE/dt = −f(ẋ). If the dissipative force is such that f(ẋ)≠0, then no Lagrangian can satisfy both ∂L/∂f = f(ẋ) and the equation of motion in the form mẍ+f(ẋ)/ẋ+dV/dt = 0.(AIP)