Gauge-invariant quantum gravitational corrections to correlation functions

Abstract

Abstract.A recent proposal for gauge-invariant observables in inflation [R. Brunetti et al., JHEP 1608 032] is examined. We give a generalisation of their construction to general background spacetimes. In flat space, we calculate one-loop graviton corrections to a scalar two-point function in a general gauge for the graviton. We explicitely show how the gauge-dependent terms cancel between the usual selfenergy contributions and the additional corrections inherent in these observables. The one-loop corrections have the expected functional form, contrary to another recently studied proposal for gauge-invariant observables [M. B. Fröb, Class. Quant. Grav. 35 (2018) 035005] where this is not the case. Furthermore, we determine the oneloop graviton corrections to the four-point coupling of the gauge-invariant scalar field, and the corresponding running of the coupling constant induced by graviton loops. Interestingly, the β function is negative for all values of the non-minimal coupling of the scalar field to curvature.

Graviton corrections to the Newtonian potential using invariant observables

“…When one wants to obtain the effects of graviton loops, however, one leaves the realm of linear perturbations and has to include non-linear self-interactions of the graviton, whence the Bardeen variables are not invariant observables anymore. To determine a gauge-invariant observable corresponding to the Newtonian potential, we follow instead the recent proposal [44] and its extensions [45][46][47][48], where relational observables for the gravitational field were constructed to all orders in perturbation theory, and which at linear order reduce to the Bardeen variables. As with all relational approaches, these observables are given by the value of one dynamical field of the theory at the point where another dynamical field has a given value, i.e., the value of one field in relation to a second one.…”

One-loop quantum gravitational backreaction on the local Hubble rate

“…A way out of this dilemma is given by constructing the scalars (in perturbation theory) as solutions of a scalar differential equation, which is fulfilled in the background spacetime. For perturbations around Minkowski spacetime in Cartesian coordinates [48], or more generally around arbitrary spacetimes in harmonic coordinates, we simply impose∇ 2X (α) [g] = 0 ,…”

“…This seems especially suited for describing physical particles carrying their own gravitational field, which must be included to obtain a gauge-invariant description. Another proposal, suitable for more general constructions, was recently made by Brunetti et al [47] and generalised by Fröb and Lima [48,49]. This proposal describes observables in a physical (field-dependent) coordinate system, and has the added advantage that its non-localities are causal, i.e., they are restricted to the past light cone.…”

Anomalies in Time-Ordered Products and Applications to the BV–BRST Formulation of Quantum Gauge Theories

“…Lastly, we would like to apply the general theory to the case of observables in perturbative quantum gravity, of the kind considered in [20][21][22]. While it is well known that gravity is non-renormalisable as a quantum theory, one can still treat it in the sense of an effective field theory, and the perturbative expansion is well defined up to any fixed order.…”