1110.5106 (Tao Zhu et al.)

General covariant Horava-Lifshitz gravity without projectability
condition and its applications to cosmology    [PDF]

Tao Zhu, Fu-Wen Shu, Qiang Wu, Anzhong Wang

We consider an extended theory of Horava-Lifshitz gravity with the detailed
balance condition softly breaking, but without the projectability condition.
With the former, the number of independent coupling constants is significantly
reduced. With the latter and by extending the original foliation-preserving
diffeomorphism symmetry $ {{Diff}}(M, {\cal{F}})$ to include a local U(1)
symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related
to them disappear, including the instability, strong coupling, and different
speeds in the gravitational sector. When the theory couples to a scalar field,
we find that the scalar field is not only stable in both the ultraviolet (UV)
and infrared (IR), but also free of the strong coupling problem, because of the
presence of high-order spatial derivative terms of the scalar field.
Furthermore, applying the theory to cosmology, we find that due to the
additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is
necessarily flat. We also investigate the scalar, vector, and tensor
perturbations of the flat FRW universe, and derive the general linearized field
equations for each kind of the perturbations.

View original: http://arxiv.org/abs/1110.5106