Classical-Quantum correspondence in a 2d universe with and without a scalar field

In this talk I will briefly describe what 2d quantum gravity is and what makes it interesting. I will then show a reasonable correspondence between classical and quantum probability distributions for the circumference of the model 2d universe described by a Lagrangian with just a gravitational part. Then I will go on to how I introduced a homogeneous scalar field in the universe and its role as an internal clock. I then utilized this internal clock to analyze the different possible evolutions of the model 2d universe.