On the smallness of the cosmological constant

Abstract

We investigate the possible values of the cosmological constant allowed by quantum cosmology. If we formulate quantum cosmology respecting the causal nature of fundamental equations in the semiclassical regime of the universe, then any classical universe should have at least one symmetric surface on which every component of the extrinsic curvature vanishes. Combined with the Hamiltonian constrain, this implies that the allowed values of the cosmological constant are bounded from above. Applying this argument to the Robertson- Walker Universe, we obtain the theoretical upperbound for the cosmological constant, being of order (H0 / c)2 . This upperbound can also be interpreted as being determined by the adiabatic Schwarzshild radius of the whole universe. In this way, the question as to why the cosmological constant is so small is reduced to the question, why there is so much matter in our universe.