Some remarks on high derivative quantum gravity

We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a diffeomorphism invariant local action. In particular, we consider the super-renormalizable case with a large number of metric derivatives in the action. The structure of ultraviolet divergences is analyzed in some detail. We show that they are independent of the gauge fixing condition and the choice of field reparametrization. The cosmological counterterm is shown to vanish under certain parameter conditions. We elaborate on the unitarity problem of high derivative approaches and the distribution of masses of unphysical ghosts. We also discuss the properties of the low energy regime and explore the possibility of having a multi-scale gravity with different scaling regimes compatible with Einstein gravity at low energies. Finally, we show that the ultraviolet scaling of matter theories is not affected by the quantum corrections of high derivative gravity. As a consequence, asymptotic freedom is stable under those quantum gravity corrections. Introduction The formulation of a consistent theory of Quantum Gravity is still one of the major challenges in theoretical physics. One of the main fundamental problems is that there is no experimental evidence of any Quantum Gravity effect [1], whereas the classical theory covers from cosmology to current precision tests with great success. The situation is considerably more dramatic that for Quantum Electrodynamics at the end of the forties. The reason being that in the last case, although the theory was not completely consistent, there was experimental evidence on the existence of relativistic quantum effects associated to electron dynamics. Nature provided confidence on the co-existence of special relativity and quantum mechanics although field theory was not yet at sight. An analogous conviction does not exist 1 On leave from Tomsk State Pedagogical Institute, Tomsk, 634041, Russia