Incorporating stochastic effects into the Wheeler-DeWitt equation

I will briefly discuss the main motivations for considering a quantum theory of gravity. Using a 3+1 decomposition of General Relativity (GR), I will describe the Hamiltonian formulation of GR, focusing on the Hamiltonian and momentum constraints. I will also talk about the meaning of the problem of time, and through the canonical quantization program, I will discuss the origin of the Wheeler-DeWitt equation. I will review basic notions of dynamical collapse models, and some proposed applications of these models within a cosmological context. I will discuss a toy model in which one incorporates the stochastic effects due to collapse models in the Wheeler-DeWitt equation, by a convenient choice of the coordinate which acts as a clock. I will show how the stochastic effects allow a mechanism for the emergence of a cosmological constant.