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Gauge-invariant quantum gravitational corrections to correlation functions

Markus B. Fröb
(
- York U., England, Dept. Math.
)

Oct 2, 2017

30 pages

Published in:

Class.Quant.Grav. 35 (2018) 5, 055006

Published: Feb 1, 2018

e-Print:

1710.00839 [gr-qc]

DOI:

10.1088/1361-6382/aaa74c

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Abstract: (IOP)

A recent proposal for gauge-invariant observables in inflation (Brunetti et al 2016 J. High Energy Phys. JHEP08(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 (Fröb 2018 Class. Quantum Grav. 35 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 β function is negative for all values of the non-minimal coupling of the scalar field to curvature.

Note:

34 pages, 1 figure, matches published version

perturbative quantum gravity
relational observables
renormalisation
invariance: gauge
gravitation: correction
field theory: scalar
quantum gravity: correction
two-point function: scalar
coupling: scalar
space-time: background

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