Extension of unimodular gravity and the cosmological constant

A new way is proposed to cancel the cosmological constant. The proposal involves the metric determinant acting as a type of self-adjusting $q$-field without need of a fine-tuned chemical potential. Since the determinant of the metric now plays a role in the physics, the allowed coordinate transformations are restricted to those with unit Jacobian. This approach to the cosmological constant problem is, therefore, similar to the unimodular-gravity approach of the previous literature. The resulting cosmology has been studied and the obtained results show the natural cancellation of an initial cosmological constant if quantum-dissipative effects are included.