Minisuperspace Approach Research Articles

Wave functions of induced 2D gravity

We consider induced 2D gravity in the minisuperspace approach. The general solution of the Wheeler-DeWitt equation is given in terms of different kinds of Bessel functions of purely real or imaginaryorders. We study the properties of the corresponding probability distributions finding a kind of phase transition at the critical point v = 0. We also discuss the validity of the minisuperspace approximation.

COSMIC TIME IN QUANTUM COSMOLOGY: INFLATION-COMPACTIFICATION AS A QUANTUM EFFECT

We consider 1+D-dimensional, toroidally compact Kaluza-Klein theories. In the context of the minisuperspace approach of quantum cosmology, we solve the Wheeler-DeWitt equation in the presence of a negative cosmological constant and dust. Then, it is found that the quantum effects stabilize the volume of the Universe, so that there can be an avoidance of the cosmological singularity. Although cosmic time does not appear explicitly in the Wheeler-DeWitt equation, we find that a cosmic time dependence appears for the expectation values of certain variables. This result is obtained when proper care of some subtle points concerning the definition of averages in this model is taken. The stabilization of the volume, when there is anisotropy in the evolution of the Universe (which turns out to be quantized), is consistent with another effect we find: the existence of a “quantum inflationary phase” for some dimensions and simultaneously the existence of a “quantum deflationary contraction” for the rest.

Path integrals and unitarity in quantum cosmology

We explore a simple cosmological model in the minisuperspace approach. The global structure of the model leads to subtleties in its quantization which are treated using the affine, rather than the Heisenberg, algebra. We develop a path-integral formulation for this algebra, and apply it to our cosmological model. We investigate the Friedmann-Robertson-Walker universe with a scalar field as source and discuss in detail the constraint that the universe have positive radius.

Wavefunction of the universe for N=2 6D supergravity

The wavefunction of the universe for N=2 6D supergravity is calculated numerically using a minisuperspace approach. When compared with the solution of the classical equations it is found that the resulting evolution of the universe is of Friedmann form with the radius of the internal space performing damped oscillations about a constant value.