Emergence of time in power-counting renormalizable Riemannian theory of gravity

We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e., locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as effective properties at long distances. On the other hand, at short distances, higher derivative terms compatible with the Riemannian diffeomorphism become important and the system is described by a power-counting renormalizable Riemannian theory.