Is the massive graviton a viable possibility?

In this talk we discuss the scenario of multigravity according to which the gravity we observe in intermediate scales (1mm< r < 10²⁶cm) is mediated by both a massless graviton and one or more of ultralight spin-2 states. We present how this can be realized in a five dimensional brane-world theory with flat branes and the complications associated with the extra polarizations of the massive gravitons (van Dam-Veltman-Zakharov discontinuity) and the ghost radions corresponding to the fluctuations of the negative tension branes present in these models. We then show how we can construct models of AdS₄ branes instead with exclusively positive tension and demonstrate how the van Dam-Veltman-Zakharov no-go theorem can be circumvented in curved space. These models, although they are consistent, face phenomenological problems related to the presence of a remnant negative cosmological constant on the branes. We finally present how we can obtain the same constructions in six dimensions with flat positive tensions branes only, in a manner that they are both theoretically consistent and phenomenologically acceptable. The latter come in two copies each and offer the first problem-free realization of the multigravity scenario.