Is there a vacuum structure in quantum gravity ?

We review the implications of topological density terms (total derivatives) in the Lagrangian density of a few quantum mechanical models as well as in the QCD. A case is made for three such terms, the Nieh-Yan, Pontryagin and Euler densities, in the quantum theory of gravity in $(1+3)$ dimensions. Associated with these are two CP-odd and one CP-even parameters. One of the CP-odd parameters, associated with the Nieh-Yan topological density, is identified with the inverse of the Barbero-Immirizi parameter already known in the theory called Loop Quantum Gravity. Thus in the quantum theory of gravity, besides two dimensionful parameters, the Newton's gravitational constant and cosomological constant, there are three other dimensionless topological coupling constants.