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Story of bimetric variational formalism
1
Hannu Nyrhinen
Story of bimetric variational formalism
JCAP05(2015)021
with Golovnev and Karciauskas
ADM analysis of bimetric variational formalism
(Golovnev, Karciauskas, HJN, 2014)
Palatini variation
On new variational principles as alternatives to the Palatini method
First, let the gravitational action
What about
?
where
(Koivisto, 2011)
In this case
Now integration by parts leaves also a and ai
dynamical and not bound
-> worse fail!
With ADM variables this is
- Metric and connection are independent.
- Vary with respect to both to get
ADM formalism
- Physical metric determines the metric structure and appears in the matter Lagrangian
- The other metric generates connection and Ricci tensor
where
The problematic term is not bound from either side -> Ghost
Finally
i.e.
This can be re-written as
- Variation is with respect to the two metrics (hence bimetric variational principle)
The end.
2010's
1900's
Bimetric variational principle for GR
C-theories
(Beltran Jimenez, Golovnev, Karciauskas, Koivisto, 2012)
(Amendola, Enqvist, Koivisto, 2011)
- The connection-generating metric allows an antisymmetric component -> Torsion propagating
- At linearised level (around Minkowski)
has ghosts. However, the linear combination
is ghost-free as long as -1 < a < 0
3D metric
Lapse
Shift
Problem!
Problem!
- Class of theories with both metric and Palatini classes as limits
- Two conformally coupled tensor fields, the physical metric and the (Levi-Civita) connection generating "metric"