Mass-Varying Massive Gravity with k-essence

For a large class of mass-varying massive gravity models, the graviton mass cannot provide the late-time cosmic expansion of the universe due to its vanishing at late time. In this work, we propose a new class of mass-varying massive gravity in which the graviton mass varies according to a kinetic term of a k-essence field. By using a more general form of the fiducial metric, we found a solution such that a non-vanishing graviton mass can drive the accelerated expansion of the universe at late time. We also perform dynamical analyses of such model and found that without introducing the k-essence Lagrangian, the graviton mass can be responsible for both dark contents of the universe, namely dark energy that drives the accelerated expansion of the universe and non-relativistic matter that plays the role of dark matter. Moreover, by including the k-essence Lagrangian, we found that it is possible to alleviate the so-called cosmic coincidence problem.Comment: 23 pages, 6 figures. Typos correctio

Cosmological model due to dimensional reduction of higher-dimensional massive gravity theory

We investigate a cosmological model resulting from a dimensional reduction of the higher-dimensional dRGT massive gravity. By using the Kaluza-Klein dimensional reduction, we obtain an effective four-dimensional massive gravity theory with a scalar field. It is found that the resulting theory corresponds to a combined description of mass-varying massive gravity and quasi-dilaton massive gravity. By analyzing the cosmological solution, we found that it is possible to obtain the late-time expansion of the universe due to the graviton mass. By using a dynamical system approach, we found regions of model parameters for which the late-time expansion of the universe is a stable fixed point. Moreover, this also provides a mechanism to stabilize the extra dimensions.Comment: 27 pages, 10 figure

Extended DBI massive gravity with generalized fiducial metric

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.Comment: 13 pages, 4 figures. Minor changes. A published versio

Black String in dRGT Massive Gravity

We present a cylindrically symmetric solution, both charged and uncharged, which is known as a black string solution to the nonlinear ghost-free massive gravity found by de Rham, Gabadadze, and Tolley (dRGT). This "dRGT black string" can be thought of as a generalization of the black string solution found by Lemos \cite{1}. Moreover, the dRGT black string solution also include other classes of black string solution such as the monopole-black string ones since the graviton mass contributes to the global monopole term as well as the cosmological constant term. To investigate the solution, we compute mass, temperature, and entropy of the dRGT black string. We found that the existence of the graviton mass drastically affects the thermodynamics of the black string. Furthermore, the Hawking-Page phase transition is found to be possible for the dRGT black string as well as the charged dRGT black string. In terms of their stability, the dRGT black string solution is thermodynamically stable for $r>r_c$ with negative thermodynamical potential and positive heat capacity while it is unstable for $r<r_c$ where the potential is positive.Comment: 17 pages, 2 figures. arXiv admin note: text overlap with arXiv:1506.0711

A class of black holes in dRGT massive gravity and their thermodynamical properties

We present exact spherical black hole solutions in de Rham, Gabadadze and Tolley (dRGT) massive gravity for a generic choice of the parameters in the theory, and also discuss the thermodynamical and phase structure of the black hole in both the grand canonical and canonical ensembles (for charged case). It turns out that the dGRT black hole solutions includes the known solutions to the Einstein field equations, such as, the monopole-de Sitter-Schwarzschild ones with the coefficients for the third and fourth terms in the potential and the graviton mass in massive gravity naturally generates the cosmological constant and the global monopole term. Furthermore, we compute the mass, temperature, and entropy of dGRT black hole solutions and also perform thermodynamical stability. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the Hawking-Page phase transition which is also true for the obtained charged black holes. Interestingly, the entropy of a black hole is unaffected and still obeys area law. In particular, our results, in the limit $m_g \rightarrow 0$, reduced exactly to \emph{vis-$\grave{a}$-vis} the general relativity results.Comment: 29 pages, 20 figures, typos fixe