Abstract:
The computation of the simplicial minisuperspace wavefunction in the case of anisotropic universes with a scalar matter field predicts the existence of a large classical Lorentzian universe like our own at late times

Abstract:
Using simplicial minisuperspace techniques we obtain a wormhole configuration, capable of modelling both a throat between two equal Euclidean and Lorentzian universes. Computing the wavefunction associated to such configuration we conclude that for Planck-size Euclidean wormholes there is a prediction of a finite non-vanishing radius of their throat, even in the absence of matter. The wavefunction associated to their Lorentzian counterparts predicts the growth of the wormhole's throat as the two Lorentzian universes expand.

Abstract:
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes either of the gravitational or of the scalar fields. In this work we propose alternatively a model where the scalar field is replaced by a massive vector field with global $U(1)$ or SO(3) symmetries.

Abstract:
We study the Robertson-Walker minisuperspace model in histories theory, motivated by the results that emerged from the histories approach to general relativity. We examine, in particular, the issue of time-reparameterisation in such systems. The model is quantised using an adaptation of reduced-state-space quantisation. We finally discuss the classical limit, the implementation of initial cosmological conditions and estimation of probabilities in the histories context.

Abstract:
A model for quantized gravity coupled to matter in the form of a single scalar field is investigated in four dimensions. For the metric degrees of freedom we employ Regge's simplicial discretization, with the scalar fields defined at the vertices of the four-simplices. We examine how the continuous phase transition found earlier, separating the smooth from the rough phase of quantized gravity, is influenced by the presence of scalar matter. A determination of the critical exponents seems to indicate that the effects of matter are rather small, unless the number of scalar flavors is large. Close to the critical point where the average curvature approaches zero, the coupling of matter to gravity is found to be weak. The nature of the phase diagram and the values for the critical exponents suggest that gravitational interactions increase with distance. \vspace{24pt} \vfill

Abstract:
We obtain a time-dependent Schrodinger equation for the Friedmann - Robertson - Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necesary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schrodinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schrodinger operator.

Abstract:
The study of a self-consistent system of interacting spinor and scalar fields within the scope of a Bianchi type I (BI) gravitational field in presence of a viscous fluid and $\Lambda$ term has been carried out. The system of equations defining the evolution of the volume scale of BI universe, energy density and corresponding Hubble constant has been derived. The system in question has been thoroughly studied qualitatively. Corresponding solutions are graphically illustrated. The system in question is also studied from the view point of blow up. It has been shown that the blow up takes place only in presence of viscosity.

Abstract:
Using the auxiliary field representation of the simplicial chiral models on a (d-1)-dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr$(AA^{\d})$ in the Lagrangian of these models by an arbitrary class function of $AA^{\d}$; $V(AA^{\d})$. This is the same method used in defining the generalized two-dimensional Yang-Mills theories (gYM_2) from ordinary YM_2. We call these models, the ``generalized simplicial chiral models''. Using the results of the one-link integral over a U(N) matrix, the large-N saddle-point equations for eigenvalue density function $\ro (z)$ in the weak ($\b >\b_c$) and strong ($\b <\b_c$) regions are computed. In d=2, where the model is in some sense related to the gYM_2 theory, the saddle-point equations are solved for $\ro (z)$ in the two regions, and the explicit value of critical point $\b_c$ is calculated for $V(B)$=Tr$B^n$ $(B=AA^{\d})$. For $V(B$)=Tr$B^2$,Tr$B^3$, and Tr$B^4$, the critical behaviour of the model at d=2 is studied, and by calculating the internal energy, it is shown that these models have a third order phase transition.