Hamiltonian Formulation of Mimetic Gravity

The Hamiltonian formulation of mimetic gravity is formulated. Although there are two more equations than those of general relativity, these are proved to be the constraint equation and the conservation of the energy-momentum tensor. The Poisson brackets are then computed and closure is proved. At the end, the Wheeler-DeWitt equation was solved for a homogeneous and isotropic universe. This was done first for a vanishing potential where agreement with the dust case was shown, and then for a constant potential.

95.35.+d
04.20.-q
04.20.Fy
04.50.Kd
energy-momentum: conservation law
tensor: energy-momentum
Hamiltonian formalism
Poisson bracket
gravitation: model

References(21)

Figures(0)

[1]

Mimetic Dark Matter

Ali H. Chamseddine
(
- American U. of Beirut and
- IHES, Bures-sur-Yvette
)
,
Viatcheslav Mukhanov
(
)

- JHEP 11 (2013) 135
•
e-Print:
- 1308.5410
•
DOI:
- 10.1007/JHEP11(2013)135

[2]

On the recently proposed Mimetic Dark Matter

Alexey Golovnev
(
- St. Petersburg State U.
)

- Phys.Lett.B 728 (2014) 39-40
•
e-Print:
- 1310.2790
•
DOI:
- 10.1016/j.physletb.2013.11.026

[3]

Dark matter as a ghost free conformal extension of Einstein theory

A.O. Barvinsky
(
- Lebedev Inst.
)

- JCAP 01 (2014) 014
•
e-Print:
- 1311.3111
•
DOI:
- 10.1088/1475-7516/2014/01/014

[4]

Cosmology with Mimetic Matter

Ali H. Chamseddine
(
- IHES, Bures-sur-Yvette and
- American U. of Beirut
)
,
Viatcheslav Mukhanov
(
- Munich U. and
- Munich, Max Planck Inst.
)
,
Alexander Vikman
(
- Munich U.
)

- JCAP 06 (2014) 017
•
e-Print:
- 1403.3961
•
DOI:
- 10.1088/1475-7516/2014/06/017

[5]

The Dynamics of general relativity

- Gen.Rel.Grav. 40 (2008) 1997-2027
•
e-Print:
- gr-qc/0405109
•
DOI:
- 10.1007/s10714-008-0661-1

[6]

Canonical Vierbein Form of General Relativity

Stanley Deser
(
- King's Coll. London
)
,
C.J. Isham
(
- King's Coll. London
)

- Phys.Rev.D 14 (1976) 2505
•
DOI:
- 10.1103/PhysRevD.14.2505

[7]

Quantized gravitational field

Julian S. Schwinger
(
- Harvard U.
)

- Phys.Rev. 130 (1963) 1253-1258,
•
DOI:
- 10.1103/PhysRev.130.1253

[8]

New Variables for Classical and Quantum Gravity

A. Ashtekar
(
- Syracuse U. and
- UC, Santa Barbara
)

- Phys.Rev.Lett. 57 (1986) 2244-2247,
- Phys. Rev. Lett. 57 ( 1986) 2244-2247
•
DOI:
- 10.1103/PhysRevLett.57.2244

[9]

New Hamiltonian Formulation of General Relativity

A. Ashtekar
(
- Syracuse U. and
- UC, Santa Barbara and
- Munich, Max Planck Inst.
)

- Phys.Rev.D 36 (1987) 1587-1602
•
DOI:
- 10.1103/PhysRevD.36.1587

[10]

: Quantized gravitational field II, Phys. Rev., 132

J.S. Schwinger

[11]

: Canonical variables for the interacting gravitational and Dirac fields

T.W.B. Kibble

- J.Math.Phys. 4 (1963) 1433

[12]

: Interacting gravitational and spinor fields, Recent Developments in General Relativity Press, New York

P.A.M. Dirac

[13]

Hamiltonian Formulation of the Theory of Interacting Gravitational and Electron Fields

J.E. Nelson
(
- Princeton U.
)
,
C. Teitelboim
(
- Princeton U.
)

- Annals Phys. 116 (1978) 86
•
DOI:
- 10.1016/0003-4916(78)90005-2

[14]

Gravitational-electromagnetic coupling and the classical self-energy problem

- Phys.Rev. 120 (1960) 313-320
•
DOI:
- 10.1103/PhysRev.120.313

[15]

: The Hamiltonian structure of space-time, General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein. Vol. 1, A. Held pp. 195-225 Press, New York

C. Teitelboim

[16]

: Canonical Gravity and Applications, Cambridge University Press

M. Bojowald

[17]

: Lectures on Quantum Mechanics, Yeshiva University Press, New York

P.A.M. Dirac

[18]

: Quantum Theory of Gravity. I The Canonical Theory

B.S. Dewitt

- Phys.Rev. 160 (1967) 5

[19]

Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity

- JHEP 12 (2014) 102
•
e-Print:
- 1404.4008
•
DOI:
- 10.1007/JHEP12(2014)102

[20]

: Quantum cosmological perfect fluid models, General Relativity and Gravitation, textbf34, , 651

F.G. Alvarenga
,
J.C. Fabris
,
N.A. Lemos
,
G.A. Monerat

[21]

: Dynamical Vacuum in Quantum Cosmology, General Relativity and Gravitation, textbf30, , 681

F.G. Alvarenga
,
N.A. Lemos