Quantum creation of an Inhomogeneous universe

In this paper we study a class of inhomogeneous cosmological models which is a modified version of what is usually called the Lemâitre-Tolman model. We assume that we have a space with 2-dimensional locally homogeneous spacelike surfaces. In addition we assume they are compact. Classically we investigate both homogeneous and inhomogeneous spacetimes which this model describe. For instance one is a quotient of the AdS4 space which resembles the BTZ black hole in AdS3. Due to the complexity of the model we indicate a simpler model which can be quantized easily. This model still has the feature that it is in general inhomogeneous. How this model could describe a spontaneous creation of a universe through a tunneling event is emphasized.