In the framework of the so called Open Quantum Relativity, we investigate a quantum universe, starting from a minimal set of variables defining the given quantum state. Entanglement between quantum states is the way to link different regions of the universe, even if (apparently) causally disconnected. As a consequence, the concept of causality results recovered and enlarged. Besides, the observed CDM model emerges from this picture, giving the possibility to realize a statistical and quantum interpretation of the cosmological constant. In particular, the novelty consists in the fact that the presently observed universe could be the result of several entanglement phenomena giving rise to a certain amount of entropy directly related to the value of cosmological constant.