Ghost-free Massive Gravity Research Articles

Non-linear electrodynamics from massive gravity

As a counterpart to the four-fermion interaction, which describes massive vector exchange at low energies, we investigate the low energy effective action of photons under exchange of a massive graviton. We show how integrating out a massive graviton leads to the most general duality-invariant vector interactions in 4D or, vice versa, how any such interactions have a natural interpretation within massive gravity. Moreover, we demonstrate how the special case of Born-Infeld theory arises from arguably the simplest graviton potential within ghost-free dRGT massive gravity.

Dynamical formulation of ghost-free massive gravity

Dynamical formulation of ghost-free massive gravity

Topological classes of higher-dimensional black holes in massive gravity

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes’ parameters. Since k and c_ 0^2c_2 m^2 appear together in the generalized free energy in the form of k +c_ 0^2c_2 m^2 , where k characterizes the horizon curvature and c_2 m^2 is the coefficient of the second term of massive potential associated with the graviton mass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghost-free massive gravity play an important role in topological classes of black holes.

Cosmological evolution in bimetric gravity: observational constraints and LSS signatures

Bimetric gravity is an interesting alternative to standard GR given its potential to provide a concrete theoretical framework for a ghost-free massive gravity theory. Here we investigate a class of Bimetric gravity models for their cosmological implications. We study the background expansion as well as the growth of matter perturbations at linear and second order. We use low-redshift observations from SnIa (Pantheon+ and SH0ES), Baryon Acoustic Oscillations (BAO), the growth (fsigma _{8}) measurements and the measurement from Megamaser Cosmology Project to constrain the Bimetric model. We find that the Bimetric models are consistent with the present data alongside the Lambda CDM model. We reconstructed the “ effective dark energy equation of state”(omega _{de}) and “Skewness”(S_{3}) parameters for the Bimetric model from the observational constraints and show that the current low-redshift data allow significant deviations in omega _{de} and S_{3} parameters with respect to the Lambda CDM behaviour. We also look at the ISW effect via galaxy-temperature correlations and find that the best fit Bimetric model behaves similarly to Lambda CDM in this regard.

Modified-gravity theories with nondynamical background fields

We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu\nu}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work. The computations show that the dynamical field equations obtained from the Lagrangian and Hamiltonian approaches are consistent with each other. Connections to Brans-Dicke theory and ghost-free massive gravity are established.

Gravitational collapse in massive gravity in de Sitter spacetime

We analyze the evolution of a homogenous and pressureless ball of dust (or ``star'') in ghost-free massive gravity on de Sitter spacetime. We find that gravitational collapse does not take place for all parameters of the massive gravity theory. For parameters where it does occur, we find the expression for the location of the apparent horizon where it crosses the surface of the star, indicating the location of the apparent horizon of the vacuum solution at that moment. We determine the Ricci curvature at the boundary of the star and extract the finite correction to the curvature of the apparent horizon due to the graviton mass. Finally, we argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star's surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.

Lorentz symmetry in ghost-free massive gravity

The role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. The result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.

Gravitational wave echoes from black holes in massive gravity

Gravitational waves are rapidly becoming a very reliable tool for testing alternative theories of gravity. In particular, features in the gravitational wave emission during black hole ringdown phase provide a direct probe of the spacetime outside the black hole. In this article, we consider black holes in ghost-free massive gravity. These black holes generically have scalar hair. We found that a simple coupling between gravitational perturbations and this scalar hair can change the quasinormal ringing of the black hole, and in particular, produce echoes in the emitted gravitational waves. This finding provides a clear-cut way to test massive gravity theory using gravitational wave observations.

Gravity with explicit spacetime symmetry breaking and the standard model extension

The Standard-Model Extension (SME) is the general phenomenological framework used to investigate Lorentz violation at the level of effective field theory. It has been used to obtain stringent experimental bounds on Lorentz violation in a wide range of tests. In the gravity sector of the SME, it is typically assumed that the spacetime symmetry breaking occurs spontaneously in order to avoid potential conflicts with the Bianchi identities. A post-Newtonian limit as well as matter-gravity couplings in the SME have been developed and investigated based on this assumption. In this paper, the possibility of using the SME to also describe gravity theories with explicit spacetime symmetry breaking is investigated. It is found that in a wide range of cases, particularly when matter-gravity couplings are included, consistency with the Bianchi identities can be maintained, and therefore the SME can be used to search for signals of the symmetry breaking. Two examples with explicit breaking are considered. The first is ghost-free massive gravity with an effective metric that couples to matter. The second is Horava gravity coupled with matter in an infrared limit.

Particle motions and gravitational lensing in de Rham-Gabadadze-Tolley massive gravity theory

We investigate gravitational lensing and particle motions around non-asymptotically flat black hole spacetime in non-linear, ghost-free massive gravity theory, called de Rham-Gabadadze-Tolley (dRGT) massive gravity. Deflection angle formulae are derived in terms of perihelion parameter. The deflection angle can be positive, zero or even negative with various perihelion distance. The negative angle reveals repulsive behaviour of gravity from a linear term $\gamma$ in the dRGT black hole solution. We also find an analytically approximated formula of deflection angle in two regimes: large and small $\gamma$ term regimes which are shown to be consistent with direct numerical integration. Null and timelike geodesic motions on equatorial plane are explored. Particle trajectories around the dRGT black hole are plotted and discussed in details.

Vierbein interactions with antisymmetric components

In this work we propose a new gravitational setup formulated in terms of two interacting vierbein fields. The theory is the fully diffeomorphism and local Lorentz invariant extension of a previous construction which involved a fixed reference vierbein. Certain vierbein components can be shifted by local Lorentz transformations and do not enter the associated metric tensors. We parameterize these components by an antisymmetric tensor field and give them a kinetic term in the action, thereby promoting them to dynamical variables. In addition, the action contains two Einstein-Hilbert terms and an interaction potential whose form is inspired by ghost-free massive gravity and bimetric theory. The resulting theory describes the interactions of a massless spin-2, a massive spin-2 and an antisymmetric tensor field. It can be generalized to the case of multiple massive spin-2 fields and multiple antisymmetric tensor fields. The absence of additional and potentially pathological degrees of freedom is verified in an ADM analysis. However, the antisymmetric tensor fluctuation around the maximally symmetric background solution has a tachyonic mass pole.

Massive mimetic cosmology

We study the first cosmological implications of the mimetic theory of massive gravity recently proposed by Chamseddine and Mukhanov. This is a novel theory of ghost-free massive gravity which additionally contains a mimetic dark matter component. In an echo of other modified gravity theories, there are self-accelerating solutions which contain a ghost instability. In the ghost-free region of parameter space, the effect of the graviton mass on the cosmic expansion history amounts to an effective negative cosmological constant, a radiation component, and a negative curvature term. This allows us to place constraints on the model parameters—the graviton mass and the Stückelberg vacuum expectation value—by insisting that the effective radiation and curvature terms be within observational bounds. The late-time acceleration must be accounted for by a separate positive cosmological constant or other dark energy sector. We impose further constraints at the level of perturbations by demanding linear stability. We comment on the possibility of distinguishing this theory from ΛCDM with current and future large-scale structure surveys.

Gravity with antisymmetric components

This work proposes a new gravitational theory formulated in terms of the vierbein field. The vierbein contains components which can be shifted by local Lorentz transformations and therefore do not show up in the spacetime metric. These components are given dynamics and become physical in our setup. They enter the massless theory in the form of an antisymmetric tensor field which makes the action reminiscent of the bosonic sector of supergravity. We then demonstrate that both the metric and the antisymmetric tensor can be made massive by adding a potential term for the vierbein. The form of this mass potential is inspired by ghost-free massive gravity. We confirm the absence of additional and potentially pathological degrees of freedom in an ADM analysis. However, at the linearized level around maximally symmetric solutions, the fluctuation of the antisymmetric tensor has a tachyonic mass pole.

Probing screening and the graviton mass with gravitational waves

Gravitational waves can probe fundamental physics, leading to new constraints on the mass of the graviton. Previous tests, however, have neglected the effect of screening, which is typically present in modified theories that predict a non-zero graviton mass. We here study whether future gravitational wave observations can constrain the graviton mass when screening effects are taken into account. We first consider model-independent corrections to the propagation of gravitational waves due to screened massive graviton effects. We find that future observation can place constraints on the screening radius and the graviton mass of – Mpc and – eV respectively. We also consider screening effects in two specific theories, ghost-free massive gravity and bigravity, that might not realize these types of propagation modifications, but that do provide analytic expressions for screening parameters relevant to our analysis allowing for more concrete results. However, the constraints we are able to place are small. The reason for this is that second- and third-generation detectors are sensitive to graviton masses that lead to very small screening radii in these particular models. The effect of screening, however, can become important as constraints on the graviton mass are improved through the stacking of multiple observations in the near future.

Mass-radius bounds in massive gravity models

The mass-radius ratio bounds of spherically symmetric static compact objects are considered in the ghost-free dRGT massive gravity. In this type of modified gravity model, the graviton has a non-zero mass leading to the naturally generated cosmological constant term. Therefore, this may bring about to an explanation for the late-time accelerated expansion of the Universe without assuming any additional dark energy. The hydrostatic equilibrium (TOV) equation in this theory is derived to describe the structure of a spherical object such as a star. In this work, the generalized Buchdahl inequalities, providing the upper and lower limits of mass-radius ratio for high density compact objects, are obtained together with their crucial constraints. Finally, for theoretical testing these results may be proved in the context of astrophysical observations.

Black hole mechanics for massive gravitons

It has been argued that black hole solutions become unavoidably time-dependent when the graviton has a mass. In this work we show that, if the apparent horizon of the black hole is a null surface with respect to a fiducial Minkowski reference metric, then the location of the horizon is necessarily time-independent, despite the dynamical metric possessing no time-like Killing vector. This result is non-perturbative and model-independent. We derive a second law of black hole mechanics for these black holes and determine their surface gravity. An additional assumption establishes a zeroth and a first law of black hole mechanics. We apply these results to the specific model of dRGT ghost-free massive gravity and show that consistent solutions exist which obey the required assumptions. We determine the time-dependent scalar curvature at the horizon of these black holes.

Deconstructing supergravity: massive supermultiplets

Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the mathcal{N}=1 Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D mathcal{N}=2 super-Maxwell theory down to 4-D mathcal{N}=1 super-Proca theory, and deconstructing linear 5-D mathcal{N}=2 supergravity down to 4-D mathcal{N}=1 Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stückelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.

On the (A)dS decoupling limits of massive gravity

We consider various decoupling limits of ghost-free massive gravity on (A)dS. The first is a decoupling limit on AdS space where the mass goes to zero while the AdS radius is held fixed. This results in an interacting massive Proca vector theory with a Λ2 ∼ (MPlm)1/2 strong coupling scale which is ghost-free by construction and yet can not be put in the form of the generalized Proca theories considered so far. We comment on the existence of a potential duality between this Proca theory and a CFT on the boundary. The second decoupling limit we consider is a new limit on dS, obtained by sending the mass towards the finite partially massless value. We do this by introducing the scalar Stückelberg field which restores the partially massless symmetry. For generic values of the parameters, only a finite number of operators enter the partially massless decoupling limit and take the form of dS Galileons. If the interactions are chosen to be precisely those of the ‘candidate’ non-linear partially massless theory, the resulting strong coupling scale has a higher value and the resulting decoupling limit includes an infinite number of interactions which we give in closed form. These interactions preserve both the linear partially massless symmetry and the dS version of the Galileon shift symmetry.

Massive spin-2 field in arbitrary spacetimes—the detailed derivation

We present the consistent theory of a free massive spin-2 field with 5 degrees of freedom propagating in spacetimes with an arbitrary geometry. We obtain this theory via linearizing the equations of the ghost-free massive gravity expressed in the tetrad formalism. The theory is parameterized by a non-symmetric rank-2 tensor whose 16 components fulfill 11 constraints implied by the equations. When restricted to Einstein spaces, the theory reproduces the standard description of massive gravitons. In generic spacetimes, the theory does not show the massless limit and always propagates five degrees of freedom, even for the vanishing mass parameter. We illustrate these features by an explicit calculation for a homogeneous and isotropic cosmological background. It turns out that the spin-2 particles are always stable if they are sufficiently massive, hence they may be a part of the Dark Mater.

Time dependent geometry in massive gravity

In this paper, we will analyze a time dependent geometry in a massive theory of gravity. This will be done by analyzing Vaidya spacetime in such a massive theory of gravity. As gravitational collapse is a time dependent system, we will analyze it using the Vaidya spacetime in massive gravity. The Vainshtein and dRGT mechanisms are used to obtain a ghost free massive gravity, and construct such time dependent solutions. Singularities formed, their nature and strength will be studied in detail. We will also study the thermodynamical aspects of such a geometry by calculating the important thermodynamical quantities for such a system, and analyzing the thermodynamical behavior of such quantities.