The Cosmological Constant in Theories with Finite Spacetime

We study the role of the cosmological constant in different theories with finite space- time. The cosmological constant appears both as an initial condition and as a constant of integration. In the context of the cosmological constant problem a new model will be presented. This modification of general relativity generates a small, non-vanishing cosmological constant, which is radiatively stable. The dynamics of the expansion of the universe in this model will be analyzed. Eventually, we try to solve the emergent problems concerning the generation of accelerated expansion using a quintessence model of dark energy