We explore the cosmological solutions of classes of non-linear bigravity theories. These theories are defined by effective four-dimensional Lagrangians describing the coupled dynamics of two metric tensors, and containing, in the linearized limit, both a massless graviton and an ultralight one. We focus on two paradigmatic cases: the case where the coupling between the two metrics is given by a Pauli-Fierz-type mass potential, and the case where this coupling derives from five-dimensional brane constructions. We find that cosmological evolutions in bigravity theories can be described in terms of the dynamics of two "relativistic particles", moving in a curved Lorenzian space, and connected by some type of nonlinear "spring". Classes of bigravity cosmological evolutions exhibit a "locking" mechanism under which the two metrics ultimately stabilize in a bi-de-Sitter configuration, with relative (constant) expansion rates. In the absence of matter, we find that a generic feature of bigravity cosmologies is to exhibit a period of cosmic acceleration. This leads us to propose bigravity as a source of a new type of dark energy ("tensor quintessence"), exhibiting specific anisotropic features. Bigravity could also have been the source of primordial inflation.

We consider an extension of the Randall-Sundrum model with three parallel 3-branes in a 5-dimensional spacetime. This new construction, apart from providing a solution to the Planck hierarchy problem, has the advantage that the SM fields are confined on a positive tension brane. The study of the phenomenology of this model reveals an anomalous first KK state which is generally much lighter than the remaining tower and also much more strongly coupled to matter. Bounds on the parameter space of the model can be placed by comparison of specific processes with the SM background as well as by the latest Cavendish experiments. The model suggests a further exotic possibility if one drops the requirement of solving the hierarchy problem. In this case gravity may result from the exchange of the ordinary graviton plus an ultralight KK state and modifications of gravity may occur at both small and extremely large scales.

We explore spherically symmetric stationary solutions, generated by "stars" with regular interiors, in purely massive gravity. We reexamine the claim that the resummation of non-linear effects can cure, in a domain near the source, the discontinuity exhibited by the linearized theory as the mass m of the graviton tends to zero. First, we find analytical difficulties with this claim, which appears not to be robust under slight changes in the form of the mass term. Second, by numerically exploring the inward continuation of the class of asymptotically flat solutions, we find that, when m is "small", they all end up in a singularity at a finite radius, well outside the source, instead of joining some conjectured "continuous" solution near the source. We reopen, however, the possibility of reconciling massive gravity with phenomenology by exhibiting a special class of solutions, with "spontaneous symmetry breaking" features, which are close, near the source, to general relativistic solutions and asymptote, for large radii, a de Sitter solution of curvature ∼ m 2 .

We show that, by considering physics in dS 4 or AdS 4 spacetime, one can circumvent the van Dam -Veltman -Zakharov theorem which requires that the extra polarization states of a massive graviton do not decouple in the massless limit. It is shown that the smoothness of the m → 0 limit is ensured if the H ("Hubble") parameter, associated with the horizon of the dS 4 or AdS 4 space, tends to zero slower than the mass of the graviton m.

An extension of Hořava-Lifshitz gravity was recently proposed in order to address the pathological behaviour of the scalar mode all previous versions of the theory exhibit. We show that even in this new extension the strong coupling persists, casting doubts on whether such a model can constitute an interesting alternative to general relativity (GR).