Gauges and functional measures in quantum gravity II: higher-derivative gravity

Abstract

We compute the one-loop divergences in a higher-derivative theory of gravity including Ricci tensor squared and Ricci scalar squared terms, in addition to the Hilbert and cosmological terms, on an (generally off-shell) Einstein background. We work with a two-parameter family of parametrizations of the graviton field, and a two-parameter family of gauges. We find that there are some choices of gauge or parametrization that reduce the dependence on the remaining parameters. The results are invariant under a recently discovered "duality" that involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable.

The background scale Ward identity in quantum gravity

“…where B μ is an auxiliary bosonic field [31]. This Gaussian integral has the effect of removing the determinants of Y from the effective action.…”

“…It has been introduced in the functional RG setting in [23,24]. Its general virtues have been further discussed in [25][26][27][28][29][30][31], and it has been employed in several other explicit calculations [32][33][34][35][36]. The second step is to make sure that no dimensionful parameter enters the gauge-fixing term.…”

“…This type of gauge fixing is often used with four-derivative gravitational actions [37][38][39][40] but normally not in the Einstein-Hilbert truncation. There is, however, no fundamental reason for this, other than simplicity [31].…”

f(R,Rμν2) at one loop

“…In the context of asymptotic safety, this dependence has been explored in [51,52]. More recently, we have computed the gauge and parametrization dependence of the one-loop divergences in Einstein gravity [53] and higher-derivative gravity [54] (with four free parameters altogether). We will use this general parametrization also in this paper.…”

On avoiding Ostrogradski instabilities within Asymptotic Safety

“…As a consequence the effective average action agrees with the standard effective action in this limit, lim k→0 Γ k ≡ Γ. Finally, the framework turns out to be sufficiently flexible to probe settings where different classes of metric fluctuations are admitted by either implementing a linear split [13], an exponential split [93,94], or an ADM split [95][96][97] of the gravitational degrees of freedom. Throughout this work, we will implement a linear split, decomposing the physical metric g µν into a fixed background metricḡ µν and fluctuations h µν according to…”