Quasi-Dilaton: 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 w.r.t.
the physical ones. The field enforcing this symmetry, dubbed here
quasi-dilaton, 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 quasi-dilaton; (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 quasi-dilaton is as consistent as massive GR is. (II)
The Vainshtein mechanism is generically retained, owing to the fact that in the
decoupling limit there is an enhanced symmetry, which turns the quasi-dilaton
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.
