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Register a new userCosmological Perturbations in the Healthy Extension of Horava-Lifshitz gravity
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Added by
Robert Brandenberger
Publication date
2010
fields
Physics
and research's language is
English
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We study linear cosmological perturbations in the ``healthy extension of Horava-Lifshitz gravity which has recently been analyzed cite{BPS2}. We find that there are two degrees of freedom for scalar metric fluctuations, but that one of them decouples in the infrared limit. Also, for appropriate choices of the parameters defining the Lagrangian, the extra mode can be made well-behaved even in the ultraviolet.
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We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts spatial momenta, can be raised up to $Lambda sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared ($10^{-42}lesssim$) $c^2_s lesssim 10^{-20}$, that could be a promising candidate for the Dark Matter. Despite these advantages, the unavoidable presence of the strong coupling obscures the implementation of the original Horavas proposal on quantum gravity. Apart from the Horava-Lifshitz model, conclusions of the present work hold also for the mimetic matter scenario, where the analogue of the projectability condition is achieved by a non-invertible conformal transformation of the metric.
We investigate the linear cosmological perturbations in Hov{r}ava-Lifshitz gravity with a scalar field. Starting from the most general expressions of the metric perturbations as well as that of a canonical scalar field, we decompose the scalar, vector and tensor parts of the perturbed action. By reducing the Hamiltonian, we find that there are two independent degrees of freedom for the tensor perturbations while none for the vector perturbations. For the scalar perturbations, the remaining number of degrees of freedom, which are all gauge invariant, depends on whether the projectable condition is applied or not. For both cases, we lose the time reparametrization symmetry of any kind.
We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in Horava-Lifshitz gravity by using the obtained classical solutions. In the obtained vacuum solutions, the parameters related to the speed of the graviton and the coefficients of quartic spatial derivative terms lead to intriguing effects: the change of graviton speed yields a surplus angle and the quartic derivatives make the square of effective electric charge negative. The result of a few tests based on the geometries of a cone, an excess cone, a black string, and a charged (black) string seems suggestive. For example, the flow of constant graviton speed and variable Newtons coupling can be favored in the vicinity of IR fixed point, but the conclusion is indistinct and far from definite yet. Together with the numerous classical solutions, static or time-dependent, which have already been found, the accumulated data from various future tests will give some hints in constraining the flow patterns more deterministic.
We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly to be obtained in the presence of ordinary matter with positive energy distribution, it seems natural in Horava-Lifshitz gravity. We present the sudden disappearance and reappearance of a star image as an astrophysical effect of a surplus angle. We also consider matter configurations of all possible power law behaviors coupled to Horava-Lifshitz gravity and obtain a series of exact solutions.
We investigate the Hamiltonian structure of linearized extended Hov{r}ava- Lifshitz gravity in a flat cosmological background following the Faddeev-Jackiws Hamiltonian reduction formalism. The Hamiltonian structure of extended Hov{r}ava-Lifshitz gravity is similar to that of the projectable version of original Hov{r}ava-Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. We also find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the infrared (IR) limit, but it is coupled to the matter field in a general cosmological background. But it is necessary to go beyond linear order in order to draw any conclusion of the strong coupling problem.
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