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arXiv · 1710.00839

Gauge-invariant quantum gravitational corrections to correlation functions

Markus B. Fröb
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Abstract

A recent proposal for gauge-invariant observables in inflation [R. Brunetti et al., JHEP 1608 (2016) 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 self-energy 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. Fr\"ob, Class. Quant. Grav. 35 (2018) 035005] where this is not the case. Furthermore, we determine the one-loop 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 $\beta$ function is negative for all values of the non-minimal coupling of the scalar field to curvature.

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Markus B. Fröb. 2017-10-02. Gauge-invariant quantum gravitational corrections to correlation functions. https://doi.org/10.1088/1361-6382%2Faaa74c

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