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We argue that the van Dam-Veltman-Zakharov discontinuity arising in the $M^2 \to 0$ limit of the massive graviton through an explicit Pauli-Fierz mass term could be absent in anti de Sitter space. This is possible if the graviton can…
We obtain a new kind of $F(^{(4)}\!R,\varphi)$ modified gravity theory as an effective four-dimensional (4D) theory derived from $f(^{(5)}\!R)$ gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the…
We construct four-dimensional covariant non-linear theories of massive gravity which are ghost-free in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an effective field theory of massive…
We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short…
A covariant formulation of a theory with a massive graviton and no negative energy state has been recently proposed as an alternative to the usual General Relativity framework. For a spatially flat homogenous and isotropic universe, the…
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism,…
The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D…
Massive gravity theories have been developed as viable IR modifications of gravity motivated by dark energy and the problem of the cosmological constant. On the other hand, modified gravity and modified dark matter theories were developed…
Demanding the existence of a simple holographic $c$-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory.…
In this paper we construct higher-dimensional minimal theory of mass-varying massive gravity (MTMVMG) where the masslike scalar potential is coupled to a vielbein potential, unlike in the previous literature where it is coupled to metric,…
We study 4D systems in which parameters of the theory have position dependence in one spatial direction. In the limit where these parameters jump, this can lead to 3D interfaces supporting localized degrees of freedom. A priori, this sort…
We propose an explicit non-linear realization of massive gravity, which relies on the introduction of a spurious compact extra dimension, on which we impose half-Newmann and half-Dirichlet boundary conditions. At the linearized level, we…
We address the question whether a graviton could have a small nonzero mass. The issue is subtle for two reasons: there is a discontinuity in the mass in the lowest tree-level approximation, and, moreover, the nonlinear four-dimensional…
We show that the ghost-free models of massive gravity and their multi-graviton extensions follow from considering higher dimensional General Relativity in Einstein-Cartan form on a discrete extra dimension, according to the Dimensional…
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to…
We systematically study the most general Lorentz-violating graviton mass invariant under three-dimensional Eucledian group using the explicitly covariant language. We find that at general values of mass parameters the massive graviton has…
In a toy model of gauge and gravitational interactions in $D \ge 4$ dimensions, endowed with an invariant UV cut-off $\Lambda$, and containing a large number $N$ of non-self-interacting matter species, the physical gauge and gravitational…
A mechanism for addressing the 'decompactification problem' is proposed, which consists of balancing the vacuum energy in Scherk-Schwarzed theories against contributions coming from non- perturbative physics. Universality of threshold…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model, cascading gravity and…