Gauge-invariant quantum gravitational corrections to correlation functions

Markus B. Fröb

doi:10.1088/1361-6382/aaa74c

Gauge-invariant quantum gravitational corrections to correlation functions

Markus B. Fröb

Mathematics

Research output: Contribution to journal › Article › peer-review

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. Fröb, 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 β function is negative for all values of the non-minimal coupling of the scalar field to curvature.

Original language	English
Number of pages	30
Journal	Classical and Quantum Gravity
Volume	35
Issue number	5
DOIs	https://doi.org/10.1088/1361-6382/aaa74c
Publication status	Published - 1 Feb 2018

Bibliographical note

© 2018 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

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© 2018 IOP Publishing Ltd . This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
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Cite this

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title = "Gauge-invariant quantum gravitational corrections to correlation functions",

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{\"o}b, 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 β function is negative for all values of the non-minimal coupling of the scalar field to curvature.",

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AB - 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. Fröb, 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 β function is negative for all values of the non-minimal coupling of the scalar field to curvature.

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