On the canonical structure and extra mode of generalized unimodular gravity

Understand

We consider a recently proposed generalization of unimodular gravity, where the lapse function is constrained to be equal to a function of the determinant of the spatial metric $f(h)$, as a potential origin of a dark fluid with a generally $h$-dependent equation of state parameter.

• We establish the Hamiltonian analysis and the canonical path integral for the theory.
• All the special cases that do not match unimodular gravity involve violation of general covariance, and consequently the physical content of the theory is changed significantly.
• Particularly, the case of a constant function $f$ is shown to contain an extra physical degree of freedom in each point of space.