A WAY TO DYNAMICALLY OVERCOME THE OLD COSMOLOGICAL CONSTANT PROBLEM

The old cosmological constant problem can be solved once we require that the full standard Einstein-Hilbert Lagrangian, gravity plus matter, is multiplied by a total derivative. We analyze such a picture writing the total derivative as the covariant gradient of a new vector field (b(mu)). Like in unimodular gravity, integration constants, regenerating an effective cosmological constant, can reenter into the game depending on the dynamics of the b(mu) field. In order to fit the present universe status without fine-tunings, a full understanding of the scales related to b(mu) field dynamics has to be settled down.