Hamiltonian analysis of mimetic scalar gravity revisited

Abstract

We perform the Hamiltonian analysis of several mimetic gravity models and compare our results with those obtained previously by different authors. We verify that for healthy mimetic scalar-tensor theories the condition for the corresponding part of the Hamiltonian to be bounded from below is the positive value of the mimetic field energy density $\lambda$. We show that for mimetic dark matter possessing a shift symmetry the mimetic energy density remains positive in time, provided appropriate boundary conditions are imposed on its initial value, while in models without shift symmetry the positive energy density can be maintained by simply replacing $\lambda \to e^{\lambda }$. The same result also applies to mimetic $f(R)$ gravity, which is healthy if the usual stability conditions of the standard $f(R)$ gravity are assumed and $\lambda >0$. In contrast, if we add mimetic matter to an unhealthy seed action, the resulting mimetic gravity theory remains, in general, unstable. As an example, we consider a scalar-tensor theory with the higher-derivative term $(\square \phi {)}^2$, which contains an Ostrogradski ghost. We also revisit results regarding stability issues of linear perturbations around the FLRW background of the mimetic dark matter in the presence of ordinary scalar matter. We find that the presence of conventional matter does not revive dynamical ghost modes (at least in the UV limit). The modes, whose Hamiltonian is not positive definite, are non-propagating (have zero sound speed) and are associated with the mimetic matter itself. They are already present in the case in which the ordinary scalar fluid is absent, causing a growth of dust overdensity.

arXiv comment40 pages, 0 figures

References in corpus (42)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Can the dark energy equation-of-state parameter w be less than -1?
• The Relation between Physical and Gravitational Geometry
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Mimetic Dark Matter
• On the Extra Mode and Inconsistency of Horava Gravity
• Cosmology with Mimetic Matter
• Dust of Dark Energy
• Dark matter as integration constant in Horava-Lifshitz gravity
• Inflation in $f(R,\varphi )$-theories and mimetic gravity scenario
• Mimetic $F(R)$ gravity: inflation, dark energy and bounce
• Hamiltonian analysis of higher derivative scalar-tensor theories
• On the recently proposed Mimetic Dark Matter
• Dark energy from modified gravity with Lagrange multipliers
• Dynamical behavior in mimetic F(R) gravity
• Cosmological viable Mimetic $f(R)$ and $f(R,T)$ theories via Noether symmetry
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity
• The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
• Dark matter as a ghost free conformal extension of Einstein theory
• Imperfect Dark Matter
• Accelerating Cosmology and Phase Structure of F(R) Gravity with Lagrange Multiplier Constraint: Mimetic Approach
• Instabilities in Mimetic Matter Perturbations
• NEC violation in mimetic cosmology revisited
• On (in)stabilities of perturbations in mimetic models with higher derivatives
• Living with ghosts in Horava-Lifshitz gravity
• Higher Derivative Mimetic Gravity
• Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations
• Jeans' Ghost
• Hamiltonian Formulation of Mimetic Gravity
• Cosmological perturbations in mimetic Horndeski gravity
• Cosmological models with Lagrange Multiplier Field
• Various Hamiltonian formulations of f(R) gravity and their canonical relationships
• Caustic free completion of pressureless perfect fluid and k-essence
• Recovering P(X) from a canonical complex field
• On the stability conditions for theories of modified gravity in presence of matter fields
• Canonical Analysis of Inhomogeneous Dark Energy Model and Theory of Limiting Curvature
• Many Faces of Mimetic Gravity
• Gravity in mimetic scalar-tensor theories after GW170817
• The Universe as an Oscillator
• Linearized gravity with matter time
• Energy conditions in mimetic-$f(R)$ gravity

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• Limiting curvature mimetic gravity for group field theory condensates
• The key role of Lagrangian multiplier in mimetic gravitational theory in the frame of isotropic compact star
• Axionic cosmological constant
• Mimetic Inflation
• Towards a viable effective field theory of mimetic gravity
• Cosmological evolution of viable models in the generalized scalar-tensor theory
• Ghost from constraints: a generalization of Ostrogradsky theorem
• Topological black holes in mimetic gravity
• Structure formation in mimetic gravity
• Emergent scenario in mimetic gravity
• Multi-field Mimetic Gravity
• Dwarf Galaxies without Dark Matter: constraints on Modified Gravity
• Can Dark Matter be Geometry? A Case Study with Mimetic Dark Matter
• Black holes with Lagrange multiplier and potential in mimetic-like gravitational theory: multi-horizon black holes
• Tachyon Mimetic Inflation as an Instabilities-Free Model
• Physical Hamiltonian for mimetic gravity
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• Extensions of two-field mimetic gravity
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• Cosmology in the mimetic higher-curvature $f(R,R_{\mu \nu }{R}^{\mu \nu })$ gravity