Generalized unimodular gravity as a form of k-essence

Understand

We consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations.

• Such class of modified gravity models includes recently suggested generalized unimodular gravity (GUMG) theory and its simplest version -- unimodular gravity (UMG).
• We make these gravity models covariant by introducing four Stueckelberg fields and show that in the case of generalized unimodular gravity three out of these fields dynamically decouple.
• This means that the covariant form of generalized unimodular gravity is dynamically equivalent to k-essence theory with a specific Lagrangian which can be reconstructed from the parameters of GUMG theory.