Hamiltonian analysis of Mimetic gravity with higher derivatives

Understand

Two types of mimetic gravity models with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism.

• For the first type of mimetic gravity, the Ricci scalar only couples to the mimetic field and we demonstrate the number of degrees of freedom (DOFs) is three.
• Then in both Einstein frame and Jordan frame, we perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly coupled to the Ricci scalar.
• We show that different from previous studies working at the cosmological perturbation level, where only three propagating DOFs show up, this generalized mimetic model, in general, has four DOFs.