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2018

Hamiltonian analysis of mimetic scalar gravity revisited

Ganz, Alexander, Karmakar, Purnendu, Matarrese, Sabino et al.

Understand

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 $\lambda>0$.

Built on

J. H. Jeans, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 199
1902
Earlier work this paper cites.
E. M. Lifshitz, Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 16
1946
Earlier work this paper cites.
P. A. M. Dirac, Proc. Roy. Soc. Lond. A246
1958
Earlier work this paper cites.
R. Schon and S.-T. Yau, Commun. Math. Phys. 65
1979
Earlier work this paper cites.
E. Witten, Commun. Math. Phys. 80
1981
Earlier work this paper cites.
S. Matarrese, Proc. Roy. Soc. Lond. A401
1985
Earlier work this paper cites.
J. D. Bekenstein, Phys. Rev. D48
1993
Earlier work this paper cites.
S. M. Carroll, M. Hoffman, and M. Trodden, Phys. Rev. D68
2003
Earlier work this paper cites.
N. Deruelle, Y. Sendouda, and A. Youssef, Phys. Rev. D80
Original
2009
Earlier work this paper cites.
S. Mukohyama, Phys. Rev. D80
Original
2009
Earlier work this paper cites.
D. Blas, O. Pujolas, and S. Sibiryakov, JHEP 10
Original
2009
Earlier work this paper cites.
E. A. Lim, I. Sawicki, and A. Vikman, JCAP 1005
Original
2010
Earlier work this paper cites.
S. Capozziello, J. Matsumoto, S. Nojiri, and S. D. Odintsov, Phys. Lett. B693
Original
2010
Earlier work this paper cites.
C. Gao, Y. Gong, X. Wang, and X. Chen, Phys. Lett. B702
Original
2011
Earlier work this paper cites.
D. Blas, O. Pujolas, and S. Sibiryakov, JHEP 04
Original
2011
Earlier work this paper cites.
A. H. Chamseddine and V. Mukhanov, JHEP 11
Original
2013
Earlier work this paper cites.
A. O. Barvinsky, JCAP 1401
Original
2014
Earlier work this paper cites.
A. H. Chamseddine, V. Mukhanov, and A. Vikman, JCAP 1406
Original
2014
Earlier work this paper cites.