We investigate effects of massive graviton on the rotation curves of the Milky Way, spiral galaxies and Low Surface Brightness~(LSB) galaxies. Using a simple de Rham, Gabadadze, and Tolley (dRGT) massive gravity model, we find static spherically symmetric metric and a modified Tolman-Oppenheimer-Volkoff (TOV) equation. The dRGT nonlinear graviton interactions generate density and pressures which behave like a dark energy that can mimic the gravitational effects of a dark matter halo. We found that rotation curves of most galaxies can be fitted well by a single constant-gravity parameter $γ\sim m_{g}^{2}C \sim 10^{-28}~{\rm m^{-1}}$ corresponding to the graviton mass in the range $m_g \sim 10^{-21}-10^{-30} {\rm eV}$ depending on the choice of the fiducial metric parameter $C\sim 1-10^{18}~\text{m}$. Fitting rotation curve of the Milky Way puts strong constraint on the Yukawa-type coupling of the massive graviton exchange as a result of the shell effects.
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…
We show that the nonlinear massive gravity model of de Rham, Gabadadze, and Tolley admits exact plane gravitational wave solution whose waveform obeys the two-dimensional Helmholtz equation. The solution is valid for arbitrary values of the coefficients of the cubic and quartic terms. In the massless limit the solution reduces to the Aichelburg-Sexl metric in general relativity.
We discuss whether or not bigravity theory can be embedded into the braneworld setup. As a candidate, we consider Dvali-Gabadadze-Porrati two-brane model with the Goldberger-Wise radion stabilization. We will show that we can construct a ghost free model whose low energy spectrum is composed of a massless graviton and a massive graviton with a small mass. As is expected, the behavior of this effective theory is shown to be identical to de Rham-Gabadadze-Tolley bigravity. Unfortunately, this correspondence breaks down at a relatively low energy due to the limitation of the adopted stabilization…
This article is devoted to static spherically symmetric black hole solutions of dRGT (de Rham-Gabadadze-Tolley) massive gravity in the presence of cosmological constant. The unitary and non-unitary gauges are used to find the solutions in three, four and five dimensions. We show that there are two general classes of solutions. In one of them, the effect of massive potential is appeared as the effective cosmological constant. By investigating these solutions in different dimensions, we find an expression for effective cosmological constant in arbitrary dimensions.
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…
The quasinormal modes of a massless Dirac field in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory with asymptotically de Sitter spacetime are investigated using the Wentzel- Kramers-Brillouin (WKB) approximation. The effective potential for the massless Dirac field due to the dRGT black hole is derived. It is found that the shape of the potential depends crucially on the structure of the graviton mass and the behavior of the quasinormal modes is controlled by the graviton mass parameters. Higher potentials give stronger damping of the quasinormal modes. We compare our results to th…
We identify different helicity degrees of freedom of Fierz-Paulian massive gravity around generic backgrounds. We show that the two-parameter family proposed by de Rham, Gabadadze, and Tolley always propagates five degrees of freedom and therefore is free from the Boulware-Deser ghost. The analysis has a number of byproducts, among which (a) it shows how the original decoupling limit construction ensures ghost freedom of the full theory, (b) it reveals an enhanced symmetry of the theory around linearized backgrounds, and (c) it allows us to give an algorithm for finding dispersion relations. T…
I derive the Komar mass/function for the Schwarszchild de-Sitter (S-dS) black-hole inside the dRGT non-linear theory of massive gravity by taking the usual notion of time-like Killing vector in unitary gauge. The dRGT Komar function depends on the dynamics of the Stückelberg fields through the gauge transformation function. It goes to the standard value obtained in General Relativity (GR) if the spatial derivative of the gauge function vanishes. In such a case, the (gauge) function corresponds to the usual notion of time as in GR.
We study the static and spherical symmetric (SSS) configurations in the non-minimal model of the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a flat reference metric. Considering the modified Tolman-Oppenheimer-Volkoff (TOV) equation, the Bianchi identity, and energy-momentum conservation, we find a new algebraic equation for the radial coordinate of the reference metric. We demonstrate that this equation suggests an absence of the Vainshtein mechanism in the minimal model of the dRGT massive gravity, while it has two branches of solutions where one connects with the Schwarzschild spac…
We study the absorption of massless scalar field by two types furry charged black holes in de Rham-Gabadadze-Tolley (dRGT) theory. The absorption cross section is calculated in high frequency limit $σ_{hf}$ and low frequency limit $σ_{lf}$. We show that the high frequency limit $σ_{hf}$ is the area of shadow and the low frequency limit $σ_{lf}$ is the area of horizon. The ratio $R_{f}=\frac{σ_{hf}}{σ_{lf}}$ is used to measure the impact of charges on the absorption spectra of furry black hole. If the black hole possess an extra charge except mass, the interval value of absorption ratio $R_{f}$…
The de Rham-Gabadadze-Tolley (dRGT) black string solution is a cylindrically symmetric and static solution of the Einstein field equation with graviton mass term. For the asymptotically de Sitter (dS) solution, it is possible to obtain the black string with two event horizons corresponding to two thermodynamic systems. The Rényi entropy is one of the entropic forms which is suitable to deal with nonextensive properties of the black string. In this work, we investigated the possibility to obtain a stable black string by using the Rényi entropy in both separated and effective approaches. We foun…
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 $γ$ in the dRGT black hole solution. We also find an analytically approximated formula of deflection angle in two regimes: large and small $γ…
We present a detailed study of the Vaidya solution and its generalization in de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored with the Stückelberg fields $ϕ^a$ introduced, there is a new invariant $I^{ab}=g^{μν}\partial_μϕ^a\partial_νϕ^b$ in the massive gravity, which adds to the ones usually encountered in general relativity. There is no conventional Vaidya solution if we choose unitary gauge. In this paper, we obtain three types of self-consistent ansatz with some nonunitary gauge, and find accordingly the Vaidya, generalized Vaidya and furry Vaidya…
We present a detailed study of the static spherically symmetric solutions in de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored by introducing the Stückelberg fields $ϕ^a$, there is new invariant $I^{ab}=g^{μν}\partial_μϕ^a\partial_νϕ^b$ in the massive gravity, which adds to the ones usually encountered in general relativity (GR). In the unitary gauge $ϕ^a=x^μδ_μ^a$, any inverse metric $g^{μν}$ that has divergence including the coordinate singularity in GR would exhibit a singularity in the invariant $I^{ab}$. Therefore, there is no conventional Schwarz…
The Stückelberg analysis of nonlinear massive gravity in the presence of a general fiducial metric is investigated. We develop a "covariant" formalism for the Stückelberg expansion by working with a local inertial frame, through which helicity modes can be characterized correctly. Within this covariant approach, an extended $Λ_3$ decoupling limit analysis can be consistently performed, which keeps $\bar{R}_{μνρσ}/m^2$ fixed with $\bar{R}_{μνρσ}$ the Riemann tensor of the fiducial metric. In this extended decoupling limit, the scalar mode $π$ acquires self-interactions due to the presence of th…
The effect of massive scalar perturbations on neutral black string in de Rham-Gabadadze-Tolley (dRGT) massive gravity is investigated through the study of the quasi-normal modes~(QNMs). Due to the similarity between the equation of motion of the field in the black-string and black-hole background, similar numerical and analytical techniques can be used to explore the behaviour of the QNMs. We use the asymptotic iteration method (AIM) and the WKB method to numerically calculate the QNMs of scalar perturbation in the black string background with positive cosmological constant. High-momentum beha…
The existence of possible massive white dwarfs more than the Chandrasekhar limit ($1.45M_{\odot }$, in which $M_{\odot }$ is mass of the sun) is a challenging topic. In this regard and motivated by the important effect of massive graviton on the structure of white dwarfs we study the white dwarfs in Vegh's massive gravity which is known as one of theories of de Rham, Gabadadze and Tolley (dRGT) like massive gravity. First, we consider the modified Tolman-Oppenheimer-Volkoff equation in this theory of massive gravity and solve it numerically by using the Chandrasekhar's equation of state. Our r…
I explain in a simple and compact form the origin of the apparent loss of predictability inside the dRGT non-linear formulation of massive gravity. This apparent pathology was first reported by Kodama and the author when the stability of the Schwarzschild de-Sitter (S-dS) black-hole in dRGT was analyzed. If we study the motion of a massive test particle around the S-dS solution, we find that the total energy is not conserved in the usual sense. The conserved quantity associated with time appears as a combination of the total energy and a velocity-dependent term. If the equations of motion are …
If we apply the path integral formulation in order to analyze the particle creation process of black-holes inside the non-linear formulation of massive gravity, it is possible to demonstrate that the effect of the extra-degrees of freedom is to deform the periodicity of the poles of the propagator in the complex $t$-plane. This might create the effect of extra-particle creation process at scales where the extra-degrees of freedom become relevant. For stationary solutions, depending on the values taken by the free parameters of the theory, the periodicity structure of the propagator reveal two …
In this work, we study the thin-shell wormholes in dRGT massive gravity. In order to joint two bulks of the spacetime geometry, we first derive junction conditions of the dRGT spacetime. This results the dynamics of the spherical thin-shell wormholes in the dRGT theory. We show that the massive graviton correction term of the dRGT theory in the Einstein equation is represented in terms of the effective anisotropic pressure fluid. However, if there is only this correction term, without invoking exotic fluids, we find that the thin-shell wormholes can not be stabilized. We then examine the stabi…
We show that the reformulation of the de Rham-Gabadadze-Tolley massive gravity theory using vielbeins leads to a very simple and covariant way to count constraints, and hence degrees of freedom. Our method singles out a subset of theories, in the de Rham-Gabadadze-Tolley family, where an extra constraint, needed to eliminate the Boulware Deser ghost, is easily seen to appear. As a side result, we also introduce a new method, different from the Stuckelberg trick, to extract kinetic terms for the polarizations propagating in addition to those of the massless graviton.
We consider Lorentz-symmetry properties of the ghost-free massive gravity theory proposed by de Rham, Gabadadze, and Tolley. In particular, we present potentially observable effects in gravitational-wave propagation and in Newton's law, including Lorentz-violating signals.
Dynamical solutions are always of interest to people in gravity theories. We derive a series of generalized Vaidya solutions in the $n$-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric. Similar to the case of the Einstein gravity, the generalized Vaidya solution can describe shining/absorbing stars. Moreover, we also find a more general Vaidya-like solution by introducing a more generic matter field than the pure radiation in the original Vaidya spacetime. As a result, the above generalized Vaidya solution is naturally included in this Vaidya-like so…
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 theory's validity regime.
We propose a simple method for deriving the constraints of the de Rham-Gabadadze-Tolley model in the metric and the Lagrangian formulation, as possible as keeping the Lorentz covariance. In our formulation, it is not necessary to use the Hamilton analysis, the vielbein formulation, nor the Stuckelberg trick for showing the Boulwer-Deser ghost-freeness. It realizes the Lorentz covariant expressions of the constraints in a certain parameter region.
The Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black hole metrics appear as exact solutions in the recently formulated massive gravity of de Rham, Gabadadze and Tolley (dRGT), where the mass term sets the curvature scale. They occur within a two-parameter family of dGRT mass terms. They show no trace of a cloud of scalar graviton modes, and in the limit of vanishing graviton mass they go smoothly to the Schwarzschild and Reissner-Nordström metrics.
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
We study the $P-V$ criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all $d\geq6$-dimensional spacetime when the coupling coefficients $c_i m^2$ of massive potential satisfy some …
We study relativistic stars in the simplest model of the de Rham-Gabadadze-Tolley massive gravity which describes the massive graviton without ghost propagating mode. We consider the hydrostatic equilibrium, and obtain the modified Tolman-Oppenheimer-Volkoff equation and the constraint equation coming from the potential terms in the gravitational action. We give analytical and numerical results for quark and neutron stars and discuss the deviations compared with General Relativity and $F(R)$ gravity. It is shown that theory under investigation leads to small deviation from the General Relativi…
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham-Gabadadze-Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Minsner-Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theor…
In this report, we discuss the behavior of coordinate-time dependent lapse function of FLRW metric of an accelerated expanding universe in the de Rham-Gabadadze-Tolley massive gravity theory. We find for the conventional dRGT formalism the corresponding lapse function can exhibit unphysical behaviors in the associated parameter space with a negative cosmological-constant-like term that leads to the decelerated universe model. To solve this problem, we introduce the so-called cosmological background density parameter to the perfect fluid stress-energy tensor which induces negative pressure. It …
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…
If the kinetic interactions of a Lorentz-invariant massive graviton are Einstein-Hilbert, then the only possible potential terms free from the Boulware-Deser ghost are those of de Rham, Gabadadze and Tolley (dRGT). We point out there are other possibilities if the kinetic terms are not required to be Einstein-Hilbert. We construct pseudo-linear ghost-free potentials, terms that derive in a natural way from the linear theory. The simplicity of this approach allows us to construct diffeomorphism non-invariant higher-derivative interaction terms that do not introduce ghosts. We conjecture that th…
Stability about cosmological background solutions to the bi-metric Hassan-Rosen theory is studied. The results of this analysis are presented, and it is shown that a large class of cosmological backgrounds is classically unstable. This sets serious doubts on the physical viability of the Hassan-Rosen theory - and in turn also of the de Rham-Gadabaze-Tolley model, to which the mentioned theory is parent. A way to overcome this instability by means of curvature-type deformations is discussed.
The tunneling behavior of fermions with half-integral spin from a higher dimensional charged anti-de Sitter (AdS) black hole in de Rham, Gabadadze and Tolley (dRGT) massive gravity is investigated via a modified Hamilton-Jacobi equation. The results demonstrate that the modified thermodynamic quantities not only are related to the properties of the higher dimensional charged AdS black hole in dRGT massive gravity but also depend on the parameter $β$, the coupling constant $σ$ and the mass of emitted particles $m$. In addition, the modified Hawking temperature is higher than the original temper…
We present a non-linear analysis of perturbations around cosmological solutions in Generalised Massive gravity. This Lorentz invariant theory is an extension of de Rham, Gabadadze, Tolley massive gravity that propagates $5$ degrees of freedom while allowing stable open FLRW cosmologies. For a minimal model that supports a self-accelerating background, we study the dynamics of non-linear perturbations. We find that the equation for the scalar graviton is distinct from the analogues in Horndeski and DHOST theories. We numerically solve the equation to find a new type of nonlinear solution for th…
In this study, we demonstrate the use of physics-informed neural networks (PINNs) for computing the quasinormal modes (QNMs) of black holes in de Rham-Gabadadze-Tolley (dRGT) massive gravity. These modes describe the oscillation frequencies of perturbed black holes and are important in understanding the behavior of these objects. We show that by carefully selecting the hyperparameters of the PINN, including the network architecture and the training data, it is possible to achieve good agreement between the computed QNMs and the approximate analytical formula in the near-extremal limit for the …
We propose a new theory of massive gravity with only two propagating degrees of freedom. After defining the theory in the unitary gauge in the vielbein language, we shall perform a Hamiltonian analysis to count the number of physical degrees of freedom, and then study some phenomenologies. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham-Gabadadze-Tolley (dRGT) massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully …
We consider a manifold endowed with two different vielbeins $E^{A}{}_μ$ and $L^{A}{}_μ$ corresponding to two different metrics $g_{μν}$ and $f_{μν}$. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation $g^{μν} E^{A}{}_μ L^{B}{}_ν = g^{μν} E^{B}{}_μ L^{A}{}_ν$ can be imposed (or the "Deser-van Nieuwenhuize…
We introduce the cosmological analysis of the Dirac-Born-Infeld dRGT massive gravity theory which is a new extension of de Rham-Gabadadze-Tolley (dRGT) massive gravity. In this theory, we consider the Dirac-Born-Infeld (DBI) scalar field which is coupled to the graviton field. Moreover, we perform the cosmological background equations, and we demonstrate the self-accelerating background solutions. We show that the theory consists of self-accelerating solutions with an effective cosmological constant. In the following, we exhibit tensor perturbations analyses and achieve the dispersion relation…
We propose a nonlinear massive gravitational theory which includes $F(R)$ modifications. This construction inherits the benefits of the de Rham-Gabadadze-Tolley model and is free of the Boulware-Deser ghost due to the existence of a Hamiltonian constraint accompanied by a nontrivial secondary one. The scalar perturbations in a cosmological background can be stabilized at the linear level for a wide class of the $F(R)$ models. The linear scalar mode arisen from the $F(R)$ sector can absorb the nonlinear longitudinal graviton, and hence, our scenario demonstrates the possibility of a gravitation…
We obtain the fully covariant linearized field equations for the metric perturbation in the de Rham-Gabadadze-Tolley (dRGT) ghost free massive gravities. For a subset of these theories, we show that the non dynamical metric that appears in the dRGT setup can be completely eliminated leading to the theory of a massive graviton moving in a single metric. This has a mass term which contains non trivial contributions of the space-time curvature. We show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes …
We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and Stückelberg fields, we first clarify how the Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli mass term. Here we find that the crucial point in the proof is that there is no higher (time) derivative for the Stückelberg `scalar' field. We then analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and Tolley, and show that there is no ghost for general admissible backgrounds. In this process, we find a very nontrivial decoupling limit for general …
The basic building block for Lorentz invariant and ghost free massive gravity is the square root of the combination $g^{-1}η\,$, where $g^{-1}$ is the inverse of the physical metric and $η$ is a reference metric. Since the square root of a matrix is not uniquely defined, it is possible to have physically inequivalent potentials corresponding to different branches. We show that around Minkowski background the only perturbatively well defined branch is the potential proposed by de Rham, Gabadadze and Tolley. On the other hand, if Lorentz symmetry is broken spontaneously, other potentials exist w…
We extend the four-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity model to a general scalar massive-tensor theory in arbitrary dimensions, coupling a dRGT massive graviton to multiple scalars and allowing for generic kinetic and mass matrix mixing between the massive graviton and the scalars, and derive its Hamiltonian formulation and associated constraint system. When passing to the Hamiltonian formulation, two different sectors arise: a general sector and a special sector. Although obtained via different ways, there are two second class constraints in either of the two sectors, …
In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostr…
It is known that de Rham-Gabadadze-Tolley (dRGT) massive gravity does not permit a homogeneous and isotropic universe with flat or spherical spatial metrics. We demonstrate that a singular reference metric solves this problem in an economic and straightforward way. In the dRGT massive gravity with a singular reference metric, there are sound homogeneous and isotropic cosmological solutions. We investigate cosmologies with the static and dynamical singular reference metrics, respectively. The term like dark energy appears naturally and the universe accelerates itself in some late time evolution…
We present a thorough analysis of the cosmological perturbations in Generalised Massive Gravity. This is an extension of de Rham-Gabadadze-Tolley theory where the translation invariance in the Stückelberg field space is broken. This allows the mass parameters to be promoted to functions of the Stückelberg fields. We consider an exact cosmological background in this theory and study the stability of perturbations. We derive conditions to avoid ghost, gradient and tachyonic instability. The cosmology is an extension of the self-accelerating branch of the constant mass parameter theory, but now a…
It is known that the no-boundary proposal in the traditional Einstein gravity does not prefer inflation, that is, the probability of realizing a large number of e-folds is exponentially suppressed. This situation may be changed drastically in a class of nonlinear massive gravity theories recently proposed by deRham, Gabadadze and Tolley, called dRGT massive gravity. We show that the contribution from the massive gravity sector can enhance the probability of a large number of e-folds substantially for a sufficiently large mass parameter mg comparable to the Hubble parameter during inflation, sa…
As massive gravity and its extensions offer physically well-defined gravitational theories with a nonzero graviton mass, we present a new extension of the de Rham-Gabadadze-Tolley (dRGT)massive gravity, which is tachyonic massive gravity theory. We firstly introduce the new extension of the dRGT massive gravity, constructed by adding a tachyonic term. We then find the cosmological background equations, and present the analysis of self-accelerating solutions. We examine the tensor perturbations to calculate the dispersion relation of gravitational waves (GWs). In a special case, we consider a c…
What is the right way to interpret a massive graviton? We generalize the kinematical framework of general relativity to multiple connections. The average of the connections is itself a connection and plays the role of the canonical connection in standard General Relativity. At the level of dynamics, the simplest choice of the Einstein-Hilbert action is indistinguishable from the single-connection case. However, inspired by Weyl geometry, we show how one can construct massive gravity to all orders in perturbation theory compatible with the de Rham-Gabadadze-Tolley ghost-free model. We conclude …
