  I consider an extension of General Relativity by an auxiliary non-dynamical
dimension that enables our space-time to acquire an extrinsic curvature.
Obtained gravitational equations, without or with a cosmological constant, have
a selfaccelerated solution that is independent of the value of the cosmological
constant, and can describe the cosmic speedup of the Universe as a geometric
effect. Background evolution of the selfaccelerated solution is identical to
that of ordinary de Sitter space. I show that linear perturbations on this
solution describe either a massless graviton, or a massive graviton and a
scalar, which are free of ghosts and tachyons for certain choices of boundary
conditions. The obtained linearized expressions suggest that nonlinear
interactions should, for certain boundary conditions, be strongly coupled,
although this issue is not studied here. The full nonlinear Hamiltonian of the
theory is shown to be positive for the selfaccelerated solution, while in
general, it reduces to surface terms in our and auxiliary dimensions.
