De Sitter ground state of scalar-tensor gravity and its primordial perturbation

Scalar-tensor gravity is one of the most competitive gravity theory to Einstein's relativity. We reconstruct the exact de Sitter solution in scalar-tensor gravity, in which the non-minimal coupling scalar is rolling along the potential. This solution may have some relation to the early inflation and present acceleration of the universe. We investigated its primordial quantum perturbation around the adiabatic vacuum. We put forward for the first time that exact de Sitter generates non-exactly scale invariant perturbations. In the conformal coupling case, this model predicts that the tensor mode of the perturbation (gravity wave) is strongly depressed.