Quasidilaton: Theory and cosmology

General Relativity (GR), with or without matter fields, admits a natural extension to a scale invariant theory that requires a dilaton. Here we show that the recently formulated massive GR, minimally coupled to matter, possesses a new global symmetry related to scaling of the reference coordinates with respect to the physical ones. The field enforcing this symmetry, dubbed here quasidilaton, coincides with an ordinary dilaton if only pure gravity is considered, but differs from it when the matter Lagrangian is present. We study (1) theoretical consistency of massive GR with the quasidilaton; (2) consistency with observations for spherically symmetric sources on (nearly) flat backgrounds; (3) cosmological implications of this theory. We find that (I) the theory with the quasidilaton is as consistent as massive GR; (II) the Vainshtein mechanism is generically retained, owing to the fact that in the decoupling limit there is an enhanced symmetry, which turns the quasidilaton into a second Galileon, consistently coupled to a tensor field; (III) unlike in massive GR, there exist flat FRW solutions. In particular, we find self-accelerated solutions and discuss their quadratic perturbations. These solutions are testable by virtue of the different effective Newton's constants that govern the Hubble expansion and structure growth.