Classical and quantum cosmology in a model of two-dimensional dilaton gravity - art. no. 104012

In this work we consider some aspects of classical and quantum cosmology in a model of two-dimensional dilaton gravity due to Callan, Giddings, Harvey , and Strominger. We describe matter by a perfect dust fluid. We start by r eviewing perfect fluids in two spacetime dimensions following the standard treatment in general relativity. We obtain the equations of motion in the v elocity-potential representation and give the action that would lead to the m. We then consider the geometrodynamical formulation of the model and in p articular obtain an expression for the Hamiltonian density of the dust matt er. This turns out to be rather difficult to work with and a great simplifi cation occurs when we restrict ourselves to the homogeneous case. Furthermo re, taking the dust to be pressureless we solve the classical equations of motion for the scale factor and the dilaton field. We show that the Univers e goes through cycles of expansion and contraction. We demonstrate the abse nce of particle horizons. Next we carry out the quantization of the model i n minisuperspace and discuss its consequences for quantum cosmology. We sol ve the Wheeler-DeWitt equation in the WKB approximation and obtain the term s of order G(-1) and G(o) in the expansion in powers of the gravitational c onstant G. We show that depending on initial conditions one can obtain expa nding or contracting solutions. The Universe can, starting from some initia l state, expand to infinite size and then contract. The limitations of semi classical analysis however prevent one from following the contraction right down to zero value for the scale factor.