We discuss a scale-free model of bigravity, in which the mass parameter of the standard bigravity potential is promoted to a dynamical scalar field. This modification retains the ghost-free bigravity structure, in particular it remains free of the Boulware-Deser ghost. We investigate the theory's interaction structure, focusing on its consistent scaling limits and strong coupling scales. Furthermore we explore the model's quadratic action, both around generic background configurations and paying special attention to cosmological backgrounds and to the associated background evolution. Finally we consider the possibility of realizing a phase of late-time acceleration as well as a quasi-de Sitter inflationary stage at early times, when the promoted "mass scalar" becomes the inflaton.
Massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure can lead to an interesting interplay between the "background" and "foreground" metrics in a cosmological context. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit. Thus, solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true.
We discuss the subtle relationship between massive gravity and bimetric gravity, focusing particularly on the manner in which massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure is more delicate than currently appreciated. Specifically, this limiting procedure should not unnecessarily constrain the background metric, which must be externally specified by the theory of massive gravity itself. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit, leading to …
We define and calculate the "discharge mode" for a Schwarzschild black hole in massive electrodynamics. For small photon mass, the discharge mode describes the decay of the electric field of a charged star collapsing into a black hole. We argue that a similar "discharge of mass" occurs in massive gravity and leads to a strange process of black hole disappearance.
We propose new version of massive $F(R)$ gravity which is natural generalization of convenient massive ghost-free gravity. Its Hamiltonian formulation in scalar-tensor frame is developed. We show that such $F(R)$ theory is ghost-free. The cosmological evolution of such theory is investigated. Despite the strong Bianchi identity constraint the possibility of cosmic acceleration (especially, in the presence of cold dark matter) is established. Ghost-free massive $F(R,T)$ gravity is also proposed.
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constant-like behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity will be figured out…
We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Eins…
We report here on two works on Lorentz invariant massive gravity. In the first part, we derive the decoupling limit of massive gravity on de Sitter, relying on embedding de Sitter into an higher dimensional Minkowski spacetime. This enables us to identify the unique candidate for a partially massless gravity theory, in which only four degrees of freedom propagate, although further work showed that this property does not hold beyond the decoupling limit. In the second part, we study the fate of the Vainshtein mechanism in the minimal model of massive gravity, in which we show the limits of the …
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 o…
We reconsider the possibility of a class of new kinetic terms in the first order (vielbein) formulation of massive gravity and multi-gravity. We find that new degrees of freedom emerge which are not associated with the Boulware--Deser ghost and are intrinsic to the vielbein formulation. These new degrees of freedom are associated with the Lorentz transformations which encode the additional variables contained in the vielbein over the metric. Although they are not guaranteed to be ghostly, they are nevertheless infinitely strongly coupled on Minkowski spacetime and are not part of the spin-2 mu…
Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication …
Ghost-free massive gravity models generically have a strong coupling scale of $Λ_3 =(M_{\rm Pl} m^2)^{1/3}$. However, for one of these models - `minimal massive gravity' - it is not clear what this scale is in the subset of solutions with vanishing vector modes, since there are then no interactions at the scale $Λ_3$. We show that there are always scalar-tensor interactions at a scale arbitrarily close to $Λ_3$ around the Minkowski vacuum solution. This explicitly confirms and completes previous research establishing that $Λ_3$ effectively is the maximal strong coupling scale for all ghost-fre…
We present the first example of a unitary theory of Lorentz-invariant massive gravity, with all degrees of freedom propagating on a strictly homogeneous and isotropic, self-accelerating de Sitter background. The theory is a simple extension of the quasidilaton theory, respecting the symmetry of the original theory but allowing for a new type of coupling between the massive graviton and the quasidilaton scalar.
We present the complete form of the decoupling limit of ghost-free massive gravity with a Minkowski reference metric, including the full interactions of the helicity-1 and helicity-0 modes of the massive spin-2 field. While in the metric language the square root structure of the mass terms makes it difficult to find a simple way to write down the interactions, we show that using the vierbein formulation of massive gravity, including Stueckelberg fields for both diffeomorphism and local Lorentz symmetries, we can find an explicitly resummed expression for the helicity-1 field interactions. We c…
Massive gravity in the weak field limit is described by the Fierz-Pauli theory with 5 degrees of freedom in four dimensions. In this theory, we calculate the gravitomagnetic effects (potential energy) between two point-like, spinning sources that also orbit around each other in the limit where the spins and the velocities are small. Spin-spin, spin-orbit and orbit-orbit interactions in massive gravity theory have rather remarkable, discrete differences from their counterparts in General Relativity. Our computation is applicable for large distances, for example, for interaction between galaxies…
We perform a detailed dynamical analysis of various cosmological scenarios in extended (varying-mass) nonlinear massive gravity. Due to the enhanced freedom in choosing the involved free functions, this cosmological paradigm allows for a huge variety of solutions that can attract the universe at late times, comparing to scalar-field cosmology or usual nonlinear massive gravity. Amongst others, it accepts quintessence, phantom, or cosmological-constant-like late-time solutions, which moreover can alleviate the coincidence problem. These features seem to be general and non-sensitive to the impos…
We show that, in the weak field limit, at large separations, in sharp contrast to General Relativity (GR), all massive gravity theories predict distance-dependent spin alignments for spinning objects. For all separations GR requires anti-parallel spin orientations with spins pointing along the line joining the sources. Hence total spin is minimized in GR. On the other hand, while massive gravity at small separations ($m_gr \le1.62$) gives the same result as GR, for large separations ($m_gr>1.62$) the spins become parallel to each other and perpendicular to the line joining the objects. Namely,…
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
We propose new massive gravity theories with 5 dynamical degrees of freedom. We evade uniqueness theorems regarding the form of the kinetic and potential terms by adopting the "generalized massive gravity" framework, where a global translation invariance is broken. By exploiting the rotation symmetry in the field space, we determine two novel classes of theories. The first one is an extension of generalized massive gravity with a non-minimal coupling. On the other hand, the second theory produces a mass term that is different from de Rham, Gabadadze, Tolley construction and trivially has 5 deg…
This is a heuristic introduction to massive gravity based on an analogy with perfect fluids. I will argue that massive gravity can be thought of as Einstein gravity in the presence of a medium with unusual properties.
Massive gravity in the presence of doubly coupled matter field via en effective composite metric yields an accelerated expansion of the universe. It has been recently shown that the model admits stable de Sitter attractor solutions and could be used as a dark energy model. In this work, we perform a first analysis of the constraints imposed by the SNIa, BAO and CMB data on the massive gravity model with the effective composite metric and show that all the background observations are mutually compatible at the one sigma level with the model.
The linearized equations of `New Massive Gravity' propagate a parity doublet of massive spin-2 modes in 3D Minkowski spacetime, but a different non-linear extension is made possible by `third-way' consistency. There is a `Chern-Simons-like' action, as for other 3D massive gravity models, but the new theory is `exotic': its action is parity odd. This `Exotic Massive Gravity' is the next-to-simplest case in an infinite sequence of third-way consistent 3D gravity theories, the simplest being the `Minimal Massive Gravity' alternative to `Topologically Massive Gravity'.
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General relativity, and topologically massive gravity in three dimensions.
We construct a generalized massive gravity by combining quadratic curvature gravity with the Chern-Simons term in four dimensions. This may be a candidate for the parity-odd tricritical gravity theory. Considering the AdS$_4$ vacuum solution, we derive the linearized Einstein equation, which is not similar to that of the three dimensional (3D) generalized massive gravity. When a perturbed metric tensor is chosen to be the Kerr-Schild form, the linearized equation reduces to a single massive scalar equation. At the tricritical points where two masses are equal to -1 and 2, we obtain a log-squar…
We present locally scale (Weyl) covariant generalisation of Minimal Massive Gravity theory using the language of exterior differential forms on Riemann-Cartan-Weyl space-times. The theory is expressed by a locally scale invariant action and locally scale covariant field equations are found by a first order variational formalism.
Constraint analysis of the three-dimensional massive gravity, the so- called new massive gravity, is studied in the Palatini formalism. We show that amongst 6 components of the metric, 2 are dynamical, which is compatible with the existence of one vector massive graviton in the linearized theory (Fierz-Pauli theory).
An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of gauge/gravity duality, a singular reference metric corresponds to momentum dissipations, which describes the electric and heat conductivity for normal conductors. We demonstrate in detail that the massive gravity with singular reference metric is ghost-free.
We consider a recently proposed non-minimal matter coupling in massive gravity and multi-gravity. We argue that, when formulated in terms of unconstrained vielbeins, this matter coupling contains the primary constraints necessary to remove the Boulware-Deser ghost to all orders away from the decoupling limit.
In a recent paper in EPJC March 2016, Faria has shown that quantum massive conformal gravity is renormalizable but has ghost states. We comment this paper on the aspect of renormalizability.
We study the generalized massive gravity in three dimensional flat spacetime. A massive logarithmic mode is propagating in the flat spacetime at the critical point where two masses degenerate. Furthermore, we discuss the logarithmic extension of the Galilean conformal algebra (GCA) which may arise from the exotic and standard rank-2 logarithmic conformal field theory (LCFT) on the boundary of AdS3 spacetime.
We investigate the new massive conformal gravity which is not invariant under conformal transformations, in comparison to the massive conformal gravity. We find five polarization modes of gravitational waves propagating on the Minkowski spacetimes. The stability of Minkowski spacetimes is guaranteed if the mass squared is not negative and the linearized Ricci tenor is employed to describe a massive spin-2 graviton. However, the small Schwarzschild black hole is unstable against the $s$-mode massive graviton perturbations.
Recently a new extended nonlinear massive gravity model has been proposed which includes the $F(R)$ modifications to dRGT model.We follow the $F(R)$ nonlinear massive gravity and study its implications on cosmological evolutions. We derive the critical points of the cosmic system and study the corresponding kinetics by performing the phase-plane analysis.
Recently in (Eur. Phys. J. C 76:341, 2016) [arXiv:1604.08706], Myung has suggested that the renormalizability of massive conformal gravity is meaningless unless the massive ghost states of the theory are stable. Here we show that massive conformal gravity can be renormalizable having unstable ghost states.
We perform the Hamiltonian analysis of 1+1 dimensional non-linear massive gravity studied in arXiv:1107.3820. We find the constraint structure of given theory and perform the counting of the physical degrees of freedom.
In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature. These solutions can be classified into three branches. In the first two, the massive gravity terms behave like a cosmological constant. In the third branch, the massive gravity effects can be described by a time evolving effective fluid with rather remarkable features, including the property to behave as a cosmological constant at late time.
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gra…
A proof that new massive gravity - the massive 3D gravity model proposed by Bergshoeff, Hohm and Townsend (BHT) - is the only unitary system at the tree level that can be constructed by augmenting planar gravity through the curvature-squared terms, is presented. Two interesting gravitational properties of the BHT model, namely, time dilation and time delay, which have no counterpart in the usual Einstein 3D gravity, are analyzed as well.
One of the fundamental open questions in cosmology is whether we can regard the universe evolution without singularity like a Big Bang or a Big Rip. This challenging subject stimulates one to regard a nonsingular universe in the far past with an arbitrarily large vacuum energy. Considering the high energy regime in the cosmic history, it is believed that Einstein gravity should be corrected to an effective energy dependent theory which could be acquired by gravity's rainbow. On the other hand, employing massive gravity provided us with solutions to some of the long standing fundamental problem…
A ghost free massive deformation of unimodular gravity (UG), in the spirit of {\em mimetic massive gravity}, is shown to exist. This construction avoids the no-go theorem for a Fierz-Pauli type of mass term in UG by giving up on Lorentz invariance. In our framework, the mimetic degree of freedom vanishes on-shell.
We define conserved gravitational charges in -cosmologically extended- topologically massive gravity, exhibit them in surface integral form about their de-Sitter or flat vacua and verify their correctness in terms of two basic types of solution.
We present a simplified formulation of massive gravity where the Higgs fields have quadratic kinetic term. This new formulation allows us to prove in a very explicit way that all massive gravity theories considered so far inevitably have Boulware-Deser ghost in non-trivial fluctuations of background metric.
We consider the massless limit of Higgs gravity, where the graviton becomes massive when the scalar fields acquire expectation values. We determine the Vainshtein scale and prove that massive gravity smoothly goes to General Relativity below this scale. We find that the Vainshtein scale depends on the particular action of scalar fields used to give mass to the graviton.
We study the null geodesics in a static circularly symmetric (SCS) black hole spacetime which is a solution in the $(2+1)$-dimensional massive gravity proposed by Bergshoeff, Hohm and Townsend (BHT massive gravity). We obtain analytic solutions for the null geodesic equation in the SCS black hole background and find the explicit form of deflection angles. We see that for various values of the impact parameter, the deflection angle can be positive, negative or even zero in this black hole spacetime. The negative deflection angle indicates the repulsive behavior of the gravity which comes from t…
In this paper, we study the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric resembles closely to the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is…
We compute the tree-level scattering amplitude between two covariantly conserved sources in generic Cosmological Topologically Massive Gravity augmented with a Fierz-Pauli term that has three massive degrees of freedom. We consider the Chiral Gravity limit in the anti-de Sitter space as well as the limit of Flat-Space Chiral Gravity. We show that Chiral Gravity cannot be unitarily deformed with a Fierz-Pauli mass. We calculate the non-relativistic potential energy between two point-like spinning sources. In addition to the expected mass-mass and spin-spin interactions, there are mass-spin inte…
The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black holes within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in $f(R)$ gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.
On the holographic complexity dual to the bulk action, we investigate the action growth for a shock wave geometry in a massive gravity theory within the Wheeler-De Witt (WDW) patch at the late time limit. For a global shock wave, the graviton mass does not affect the action growth in the bulk, i.e. the complexity on the boundary, showing that the action growth (complexity) is the same for both the Einstein gravity and the massive gravity. Nevertheless, for a local shock wave that depends on transverse coordinates, the action growth (complexity) is proportional to the butterfly velocity for the…
We introduce the Brans-Dick de Rham-Gabadadze-Tolley massive gravity theory which is the new extension of nonlinear massive gravity. We demonstrate a detailed study of the cosmological properties of this theory of gravity, and we show the transformation of the Jordan frame to the Einstein frame. We obtain the cosmological background equations and show the analyses of self-accelerating solutions for explaining the accelerated expansion of the Universe. In the following, we analyze the background perturbations, which consist of tensor, vector, and scalar perturbations within the framework of the…
We analyze the classical stability of Schwarzschild black hole in massive conformal gravity which was recently proposed for another massive gravity model. This model in the Jordan frame is conformally equivalent to the Einstein-Weyl gravity in the Einstein frame. The coupled linearized Einstein equation is decomposed into the traceless and trace equation when one chooses $6m^2φ=δR$. Solving the traceless equation exhibits unstable modes featuring the Gregory-Laflamme $s$-mode instability of five-dimensional black string, while we find no unstable modes when solving the trace equation. It is sh…
We study spherically-symmetric solutions in Massive Gravity generated by matter sources with polytropic equation of state. We concentrate in the non-perturbative regime where the mass term non-linearities are important, and present the main features of the solutions.
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.
In this paper, we generalize the study of the model of holographic superconductor in the excited states to the framework of massive gravity. By taking into account the effect of massive graviton, we numerically present a family of solutions of the holographic superconductor in excited states, and find that the critical temperatures can be higher due to the effect of massive graviton comparing with the superconductor in Einstein gravity. We also investigate the condensates and conductivities in the ground state and the excited states with studying various parameters that determine the framework…
We investigate the possibility of a new massive gravity theory with derivative interactions as an extension of de Rham-Gabadadze-Tolley massive gravity. We find the most general Lagrangian of derivative interactions using Riemann tensor whose cutoff energy scale is $Λ_3$, which is consistent with de Rham-Gabadadze-Tolley massive gravity. Surprisingly, this infinite number of derivative interactions can be resummed with the same method in de Rham-Gabadadze-Tolley massive gravity, and remaining interactions contain only two parameters. We show that the equations of motion for scalar and tensor m…
I review how "classical SUGRA" embeddability establishes positive energy E for D=3 topologically massive gravity (TMG), with or without a cosmological term, a procedure familiar from D=4 Einstein gravity (GR). It also provides explicit expressions for E. In contrast to GR, E is not manifestly positive, due to the peculiar two-term nature of TMG.
The existence of a ghost free theory of massive gravity begs for an interpretation as a Higgs phase of General Relativity. We revisit the study of massive gravity as a Higgs phase. Absent a compelling microphysical model of spontaneous symmetry breaking in gravity, we approach this problem from the viewpoint of nonlinear realizations. We employ the coset construction to search for the most restrictive symmetry breaking pattern whose low energy theory will both admit the de Rham-Gabadadze-Tolley (dRGT) potentials and nonlinearly realize every symmetry of General Relativity, thereby providing a …
Using the metric formalism, we study the derivative mixings of spin-2 fields in massive bi-Gravity. Necessary (but not sufficient) criteria are given for such mixings to be ghost free. Examples satisfying those criteria are studied and it is shown that in the decoupling limit they host a ghost.
We study the conserved charges of supersymmetric solutions in the topologically massive gravity theory for both asymptotically flat and constant curvature geometries.
We study van Dam-Veltman-Zakharov discontinuity in the topologically new massive gravity (TNMG). The reduction from 2 degrees of freedom to one is interpreted as van Dam-Veltman-Zakharov discontinuity appeared when going from anti-de Sitter spacetime to Minkowski spacetime in the linearized TNMG.
We present a 3-dimensional model for massive gravity with masses induced by topological (Chern-Simons) and Proca-like mass terms. Causality and unitarity are discussed at tree-level. Power-counting renormalizability is also contemplated.
We find the Gregory-Laflamme $s$-mode instability of the non-rotating BTZ black hole in new massive gravity. This instability shows that the BTZ black hole could not exist as a stable static solution to the new massive gravity. For non-rotating BTZ black string in four dimensions, however, it is demonstrated that the BTZ black string can be stable against the metric perturbation.
