Some Remarks on High Derivative Quantum Gravity

Abstract

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 superrenormalizable 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 multiscale 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.

On Newtonian singularities in higher derivative gravity models

“…Let us note that much earlier, the same result concerning the absence of Newtonian singularity has been obtained in [18,19] for a modified low-energy string effective action, which is essentially equivalent to the model of [16] and [9][10][11][12]. In the present work we shall extend this result for a set of local higher-derivative models suggested in [20].…”

“…It would be interesting and useful to understand whether a similar relation takes place for the higher derivative models of [20], especially in view of the absence of singularities that takes place for the ghost-free theory of [18,19] and [9,15,16]. In the case of fourth-order gravity, the eq.…”

“…As we have seen, this idea is not working for the cancellation of Newtonian singularity and one can easily show that it is nor working also for the super-renormalizable models suggested in [20]. The consideration presented above shows that the role of the ghosts and normal particles in the singularity cancellation requires that these particles should actually enter by the pairs of scalar particle plus tensor ghost and tensor particle plus scalar ghost.…”

“…The problem of ghosts has a long and interesting history, but since it is not the subject of the present work, let us just readdress the reader to the recent papers [25,26] of one of us for a brief review and further references. The models of [20] were promoted to the ghost-free non-polynomial form in [16], but the quantum properties of this version, such as (super)renormalizability are not clear yet. One can see the discussion of this question in [25,26] and also parallel consideration in [27,28].…”

“…The functions F 1,2,3 used in [16] to avoid ghosts are exponential, quite different from the asymptotically logarithmic form factors of one-loop semiclassical terms of [21,22], from the constants in the renormalizable gravity case [23], and from the polynomial form of a superrenormalizable quantum gravity models of [20]. As we have mentioned above, recently the exponential form of these functions has been used in [10][11][12] to cure the singularity of the Newtonian point-like solution.…”