Quantum stationary geometries and avoidance of singularities

A recent approach to quantum gravity leading to the concept of quantum stationary geometries is reviewed. A stationary states equation is presented for: (a) homogeneous relativistic cosmologies of the various Bianchi types; (b) a Friedmann universe filled with a massless scalar field. The equation is solved near the singularity to show that stationary states avoid the singularity. The result is discussed and compared with other approaches