Physical Hamiltonian for mimetic gravity

TL;DR

This paper derives a gauge-fixed canonical Hamiltonian for mimetic gravity with higher derivatives, revealing a conserved physical Hamiltonian and providing insights into perturbations around various spacetimes.

Contribution

It presents the first explicit derivation of a gauge-fixed canonical Hamiltonian for mimetic gravity including higher derivatives, with applications to different spacetime backgrounds.

Findings

Conserved physical Hamiltonian combining GR Hamiltonian constraint and expansion scalar.

Reduced symplectic structure yields Dirac brackets.

Explicit canonical equations for perturbations around Minkowski, cosmological, and spherical spacetimes.

Abstract

Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $\phi$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $\phi=t$. This reduced action reveals (i) a non-vanishing conserved physical Hamiltonian that is a sum of two terms, the expression for the Hamiltonian constraint of general relativity and a function of the expansion scalar, and (ii) a reduced symplectic structure that geometrically provides the Dirac brackets. As applications of our general analysis, we compute the physical Hamiltonians and canonical equations for perturbations around Minkowski spacetime, homogeneous cosmologies, and spherically symmetric spacetimes.