The unavoidable de Sitter fate of a scale-invariant universe

We consider a very general scale-invariant scalar-tensor theory of gravity and its flat cosmological solutions. We show that any stable configuration with non-degenerate gravitational dynamics carries a non-vanishing cosmological constant, unless the quartic self-coupling of the scalar field vanishes. Since this condition is not protected against radiative corrections, a residual cosmological constant is expected as a generic and robust prediction of this class of theories. This result suggests that dark energy may be a natural consequence of an early scale-invariant phase of the Universe.