Hamiltonian analysis of Mimetic gravity with higher derivatives

Abstract

Two kinds of mimetic gravity model with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism. We first perform the Hamiltonian analysis for the mimetic gravity with a general higher derivative function and show the degrees of freedom (DOFs) is 3 which is consistent with the previous result of the Hamiltonian analysis at the perturbation level. We then perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly couples to the Ricci scalar in both Einstein frame and Jordan frame, and we show that different from our previous research at the cosmological perturbation level where only 3 propagating DOFs show up, this generalized mimetic model in general has 4 DOFs. To solve this discrepancy, we find out that the DOFs is reduced to 3 in the unitary gauge while the extra mode is eliminated by appropriate boundary conditions (homogeneous scalar field profile). What makes the system so special is that the Dirac matrix becomes singular in the special unitary gauge, generating extra secondary constraints and reducing the number of DOFs, so we give a similar but simpler example to illustrate how gauge choice affects the number of secondary constraints and the DOFs when the rank of the Dirac matrix is gauge dependent.

Hamiltonian analysis of mimetic scalar gravity revisited

“…Therefore, the model has three degrees of freedom one of which is that of the mimetic field ϕ. We see that the higher-derivative term does not introduce an extra degree of freedom, as was shown in [12,13,25]. 6 The question is whether the mimetic constraint can cure the instability of the higher-derivative theory.…”

“…( 122), the model has a singular point G(ϕ) = 1 3 (observed and discussed in detail e.g. in [25]), in which the first two terms vanish. This results in the fact that in homogeneous backgrounds in which ϕ is identified with the time flow (ϕ = t) the number of the degrees of freedom in this model reduces from three to two.…”

“…The Hamiltonian analysis of mimetic gravity with a generic term F ( ϕ) in the action has been carried out in [12,25]. However, since it is only possible to write down the Hamiltonian implicitly in terms of a general inverse function of F , it is quite involved to analyze its stability properties.…”

“…However, the stability analysis of this Hamiltonian has not been carried out therein. The full Hamiltonian analysis for a simple mimetic dark matter model was carried out in [7,24] and extended in [12] to mimetic gravity actions involving an arbitrary function F ( ϕ) of the mimetic scalar field and further generalized in [25]. As we already mentioned, the main conclusion was that the stability of the mimetic system requires that the energy density of the mimetic dust is non-negative.…”

Flat and bent branes with inner structure in two-field mimetic gravity

“…With the appropriate choice of the potential, it is possible to provide an inflationary mechanism and a bouncing universe within this framework [21]. Therefore, this stimulates some interests in phenomenology and its observational viability [23][24][25][26][27][28][29][30], and leads to the Hamiltonian analyses of different mimetic models [31][32][33][34][35]. Mimetic gravity in various modified gravity theories has also been widely discussed in [36][37][38][39][40][41][42][43][44][45][46].…”