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Register a new userNew Cosmological Solutions in Massive Gravity
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We find new, simple cosmological solutions with flat, open, and closed spatial geometries, contrary to the previous wisdom that only the open model is allowed. The metric and the St{u}ckelberg fields are given explicitly, showing nontrivial configurations of the St{u}ckelberg in the usual Friedmann-Lema^{i}tre-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can accommodate inhomogeneous dust collapse represented by the Lema^{i}tre-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.
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We have discussed a particular class of exact cosmological solutions of the 4-dimensional low energy string gravity in the string frame. In the vacuum without matter and the 2-form fields, the exact cosmological solutions always give monotonically shrinking universes if the dilaton field is not a constant. However, in the presence of the 2-form fields and/or the radiation-like fluid in the string frame, the exact cosmological solutions show a minimum size of the universe in the evolution, but with an initial cosmological curvature singularity in the string frame.
A phase of massive gravity free from pathologies can be obtained by coupling the metric to an additional spin-two field. We study the gravitational field produced by a static spherically symmetric body, by finding the exact solution that generalizes the Schwarzschild metric to the case of massive gravity. Besides the usual 1/r term, the main effects of the new spin-two field are a shift of the total mass of the body and the presence of a new power-like term, with sizes determined by the mass and the shape (the radius) of the source. These modifications, being source dependent, give rise to a dynamical violation of the Strong Equivalence Principle. Depending on the details of the coupling of the new field, the power-like term may dominate at large distances or even in the ultraviolet. The effect persists also when the dynamics of the extra field is decoupled.
Generic massive gravity models in the unitary gauge correspond to a self-gravitating medium with six degrees of freedom. It is widely believed that massive gravity models with six degrees of freedom have an unavoidable ghost-like instability; however, the corresponding medium has stable phonon-like excitations. The apparent contradiction is solved by the presence of a non-vanishing background pressure and energy density of the medium that opens up a stability window. The result is confirmed by looking at linear stability on an expanding Universe, recovering the flat space stability conditions in the small wavelength limit. Moreover, one can show that under rather mild conditions, no ghost-like instability is present for any wavelength. As a result, exploiting the medium interpretation, a generic massive gravity model with six degrees of freedom is perfectly viable.
The de Rham-Gabadadze-Tolley massive gravity admits pp-wave backgrounds on which linear fluctuations are shown to undergo time advances for all values of the parameters. The perturbations may propagate in closed time-like curves unless the parameter space is constrained to a line. These classical phenomena take place well within the theorys validity regime.
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.
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