Physical Hamiltonian for mimetic gravity

Abstract

Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $\varphi$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $\varphi =t$. 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.

arXiv comment23 pages

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• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
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