The slow expansion with nonminimal derivative coupling and its conformal dual

We show that the primordial gravitational wave with scale-invariant spectrum might emerge from a nearly minkowski space, in which the gravity is asymptotic-past free. we illustrate it with a model, in which the derivative of background scalar field nonminimally couples to gravity. we also show that since here the tensor perturbation is dominated by its growing mode, mathematically our slowly expanding background is conformally dual to the matter contraction, but there is no the anisotropy problem.