of time in quantum theory and general relativity. Time in the latter, is a dynamical object in contrast to quantum theory, in which it is introduced as an external parameter. Quantum gravity may modify the concept of time in one or both of these theories. There are various approaches for building quantum theory of gravity. In [2], these ap- proaches are categorized in three sets. The first category is the covariant line , which is simply the quantum field theory of fluctuations over some background metric. This idea leads to higher derivative theories and string theory. The canonical line is the second approach, in which there is no need to introduce the background metric. The Hilbert space can be considered as a rep- resentation of operators corresponding to the metric or functions of it. Loop quantum gravity seems to be the latest one in this category. Finally the name sum over histories line is assigned to the third set which contains versions of Feynman’s functional integral quantization for the suggested quantum gravity theory. Discrete approaches and spinfoams formalism belong to this set. In any perturbative approach, which is attractive to particle physicists, offering a finite quantity is an important point in a theory. One of the difficulties in perturbative quantization of gravity is the negative (mass–) dimension of gravity coupling, i.e. Newton constant, which leads to divergences at short distances or high energies. Although renormalization of divergences necessarily does not result in a covariant formalism, but would be a vital issue in the suggested quantum gravity theory. In this context, Weinberg’s asymptotic safety suggestion in 1979 [3] based on the existence of a finite number of non–Gaussian fixed points, for which the renormalization group (RG) flow attracted by them at infinity, is notable. Many successful research works have been done on the existence of these fixed points (see references in [4]). The attraction of the RG–flow to these non–Gaussian UV fixed points at short distances, protects the theory from divergences in that limit. In 1998, Reuter suggested the truncated exact renormalization group (ERG) method [5] for probing non–Gaussian fixed points, where the trajectories of running essential gauge couplings lie on the finite dimensional subspace of the theory space [6]. It is known that the β -functions give us running couplings of the theory which are screened or anti–screened by loop corrections 2