We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension. The worldvolume theory gives rise to the correct 4D potential at short distances whereas at large distances the potential is that of a 5D theory. We discuss some phenomenological issues in this framework.

We construct four-dimensional covariant non-linear theories of massive gravity which are ghostfree in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an effective field theory of massive gravity. We show that away from the decoupling limit the Hamiltonian constraint is maintained at least up to and including quartic order in non-linearities, hence, excluding the possibility of the Boulware-Deser ghost up to this order. We also show that the same remains true to all orders in a similar toy-model. Introduction:Whether there exist a consistent extension of General Relativity by a mass term is a basic question of a classical field theory. A small graviton mass could also be of a significant physical interest, notably for the cosmological constant problem.A ghost-free linear theory of massive spin-2 -the FierzPauli (FP) model [1] -had been notoriously hard to generalize to the nonlinear level [2]: the Hamiltonian constraint gets lost in general and, as a result, the sixth degree of freedom -the Boulware-Deser (BD) ghostemerges as a mode propagating on otherwise physically meaningful local backgrounds (e.g., on a background of a lump of matter). Part of this problem can be seen in the effective field theory (EFT) approach to massive gravity [3] in the decoupling limit [3,4]. There, the problem manifests itself in the Lagrangian for the helicity-0 component of the massive graviton. This Lagrangian generically contains nonlinear terms with more than two time derivatives. The latter give rise to the sixth degree of freedom on local backgrounds, while in general, these terms lead to the loss of well-posedness of the Cauchy problem for the helicity-0 field theory [3,4].A step forward has been made recently in [5] where it was shown that: (a) the coefficients of the EFT can be chosen so that the decoupling limit Lagrangian is ghostfree; this involves choosing the "appropriate coefficients" order-by-order, and an algorithm was set for this procedure to an arbitrary order; (b) once the "appropriate coefficients" are chosen in the effective Lagrangian, in the decoupling limit only a few terms up to the quartic order survive, all the higher order terms vanish identically. Moreover, the surviving terms are unique as their structure is fixed by symmetries [5,6].In the present work we build on the above two points, and go far beyond them. In particular: (1) We construct Lagrangians that automatically produce the "appropriate coefficients" once expanded in powers of the fields; these give rise to theories that are ghost-free automatically to all orders in the decoupling limit. (2) Using the obtained Lagrangians we study the issue of the BD ghost away from the decoupling limit; we show that the Hamiltonian constraint is maintained at least up to and including

We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients, and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghost-like pathologies in these interactions disappear for special choices of the polynomial interactions, and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear, and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit, and for the Boulware-Deser problem.

We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.

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 theory of a massive graviton is not defined unambiguously. First, we reiterate the old argument that for the vanishing graviton mass the lowest tree-level approximation breaks down since the higher order corrections are singular in the graviton mass. However, there can exist nonperturbative solutions which correspond to the summation of the singular terms, and these solutions are continuous in the graviton mass. Furthermore, we study a completely nonlinear and generally covariant five-dimensional model which mimics the properties of the four-dimensional theory of massive gravity. We show that the exact solutions of the model are continuous in the mass, yet the perturbative expansion exhibits the discontinuity in the leading order and the singularities in higher orders as in the four-dimensional case. Based on exact cosmological solutions of the model we argue that the helicity-zero graviton state which is responsible for the perturbative discontinuity decouples from the matter in the limit of vanishing graviton mass in the full classical theory.

We show that in theories with large extra dimensions forces mediated by a bulk dilaton and bulk gauge fields may be parametrically (exponentially) weaker than gravity due to the suppression of their wave-functions on a brane. This is the case when dilaton gets stabilized by certain strongly coupled dynamics on the brane, or the bulk gauge symmetries are spontaneously broken by the Higgs mechanism on the worldvolume. At distances smaller than the size of a largest extra dimension these particles produce the force-law which decreases with distance faster than highdimensional gravity. For a millimeter size extra dimensions predicted deviations are in the range which may be detected in sub-millimeter gravity measurements.

We explore the cosmological solutions of a recently proposed extension of General Relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard FRW evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low density regime each domain of the size of the inverse graviton mass has essentially non-FRW cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers.Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.

We generalize the mechanism proposed in a previous paper and show that a four-dimensional relativistic tensor theory of gravitation can be obtained on a delta-function brane in flat infinite-volume extra space. In particular, we demonstrate that the induced Ricci scalar gives rise to Einstein's gravity on a delta-function type brane if the number of space-time dimensions is bigger than five. The bulk space exhibits the phenomenon of infrared transparency. That is to say, the bulk can be probed by gravitons with vanishing four-dimensional momentum square, while it is unaccessible to higher modes. This provides an attractive framework for solving the cosmological constant problem.