4.4 Conclusions
45
of the general covariance. In a similar manner, other Lorentz-breaking gravitational
terms introduced in [74] can be treated. As a result, relaxing the condition for the
Lorentz-breaking vector to be constant, we have a theory consistent with the general
covariance requirement.
We note that the term B
μ B
ν R μν is the particular case of the term s
μν R μν discussed
in [74]. Actually, in [74], two terms are presented, so, the possible Lorentz-breaking
extension of gravity is introduced through adding the term
δS =
d
4 x
|g|(s
μν R μν + t
μνλρ R μνλρ ),
(4.21)
where s
μν , t
μνλρ are coefficients of explicit Lorentz symmetry breaking (in this
review, we consider only the zero torsion case). However, up to now the main attention
(see f.e. [92]) was paid to the s
μν term while the t
μνλρ
= 0 condition was applied.
To close the discussion of the Lorentz symmetry breaking in gravity, let us say
some words about the weak (linearized) gravity. We have noted already that, for the
specific form of the Chern–Simons coefficient, the gravitational CS term (3.6) displays Lorentz symmetry breaking. In [47], another, one-derivative Lorentz-breaking
term in the linearized gravity has been studied. In principle, much more Lorentzbreaking terms in the linearized gravity can be introduced. However, it is clear that
many studies of Lorentz symmetry breaking in gravity are still to be carried out, and
it is natural to expect that such studies will be performed in the next years.
45
of the general covariance. In a similar manner, other Lorentz-breaking gravitational
terms introduced in [74] can be treated. As a result, relaxing the condition for the
Lorentz-breaking vector to be constant, we have a theory consistent with the general
covariance requirement.
We note that the term B
μ B
ν R μν is the particular case of the term s
μν R μν discussed
in [74]. Actually, in [74], two terms are presented, so, the possible Lorentz-breaking
extension of gravity is introduced through adding the term
δS =
d
4 x
|g|(s
μν R μν + t
μνλρ R μνλρ ),
(4.21)
where s
μν , t
μνλρ are coefficients of explicit Lorentz symmetry breaking (in this
review, we consider only the zero torsion case). However, up to now the main attention
(see f.e. [92]) was paid to the s
μν term while the t
μνλρ
= 0 condition was applied.
To close the discussion of the Lorentz symmetry breaking in gravity, let us say
some words about the weak (linearized) gravity. We have noted already that, for the
specific form of the Chern–Simons coefficient, the gravitational CS term (3.6) displays Lorentz symmetry breaking. In [47], another, one-derivative Lorentz-breaking
term in the linearized gravity has been studied. In principle, much more Lorentzbreaking terms in the linearized gravity can be introduced. However, it is clear that
many studies of Lorentz symmetry breaking in gravity are still to be carried out, and
it is natural to expect that such studies will be performed in the next years.