Abstract
We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results set the stage for a project to purge gauge dependence by including quantum gravitational corrections to the source which disturbs the effective field and to the observer who measures it.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.A. Starobinsky, Spectrum of relict gravitational radiation and the early state of the universe, JETP Lett. 30 (1979) 682 [INSPIRE].
A.A. Starobinsky, Cosmic Background Anisotropy Induced by Isotropic Flat-Spectrum Gravitational-Wave Perturbations, Sov. Astron. Lett. 11 (1985) 133 [INSPIRE].
N.C. Tsamis and R.P. Woodard, Quantum gravity slows inflation, Nucl. Phys. B 474 (1996) 235 [hep-ph/9602315] [INSPIRE].
N.C. Tsamis and R.P. Woodard, The Quantum gravitational back reaction on inflation, Annals Phys. 253 (1997) 1 [hep-ph/9602316] [INSPIRE].
N.C. Tsamis and R.P. Woodard, One loop graviton selfenergy in a locally de Sitter background, Phys. Rev. D 54 (1996) 2621 [hep-ph/9602317] [INSPIRE].
L. Tan, N.C. Tsamis and R.P. Woodard, Graviton self-energy from gravitons in cosmology, Class. Quant. Grav. 38 (2021) 145024 [arXiv:2103.08547] [INSPIRE].
P.J. Mora, N.C. Tsamis and R.P. Woodard, Hartree approximation to the one loop quantum gravitationalcorrection to the graviton mode function on de Sitter, JCAP 10 (2013) 018 [arXiv:1307.1422] [INSPIRE].
L. Tan, N.C. Tsamis and R.P. Woodard, How Inflationary Gravitons Affect Gravitational Radiation, arXiv:2107.13905 [INSPIRE].
S. Park, T. Prokopec and R.P. Woodard, Quantum Scalar Corrections to the Gravitational Potentials on de Sitter Background, JHEP 01 (2016) 074 [arXiv:1510.03352] [INSPIRE].
S.-P. Miao and R.P. Woodard, The Fermion self-energy during inflation, Class. Quant. Grav. 23 (2006) 1721 [gr-qc/0511140] [INSPIRE].
S.P. Miao, Quantum Gravitational Effects on Massive Fermions during Inflation I, Phys. Rev. D 86 (2012) 104051 [arXiv:1207.5241] [INSPIRE].
S.P. Miao and R.P. Woodard, Gravitons Enhance Fermions during Inflation, Phys. Rev. D 74 (2006) 024021 [gr-qc/0603135] [INSPIRE].
E.O. Kahya and R.P. Woodard, Scalar field equations from quantum gravity during inflation, Phys. Rev. D 77 (2008) 084012 [arXiv:0710.5282] [INSPIRE].
E.O. Kahya and R.P. Woodard, Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation, Phys. Rev. D 76 (2007) 124005 [arXiv:0709.0536] [INSPIRE].
K.E. Leonard and R.P. Woodard, Graviton Corrections to Vacuum Polarization during Inflation, Class. Quant. Grav. 31 (2014) 015010 [arXiv:1304.7265] [INSPIRE].
C.L. Wang and R.P. Woodard, Excitation of Photons by Inflationary Gravitons, Phys. Rev. D 91 (2015) 124054 [arXiv:1408.1448] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, Electrodynamic Effects of Inflationary Gravitons, Class. Quant. Grav. 31 (2014) 175002 [arXiv:1308.3453] [INSPIRE].
S. Boran, E.O. Kahya and S. Park, Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background, Phys. Rev. D 90 (2014) 124054 [arXiv:1409.7753] [INSPIRE].
S. Boran, E.O. Kahya and S. Park, Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background. II. Kinetic conformal cross terms, Phys. Rev. D 96 (2017) 025001 [arXiv:1704.05880] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, Single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on a de Sitter background, Phys. Rev. D 101 (2020) 106016 [arXiv:2003.02549] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, One-loop Graviton Corrections to Conformal Scalars on a de Sitter Background, Phys. Rev. D 103 (2021) 105022 [arXiv:2007.10395] [INSPIRE].
S.L. Detweiler, Pulsar timing measurements and the search for gravitational waves, Astrophys. J. 234 (1979) 1100 [INSPIRE].
D.R. Lorimer, Binary and Millisecond Pulsars, Living Rev. Rel. 11 (2008) 8 [arXiv:0811.0762] [INSPIRE].
J. Garriga and T. Tanaka, Can infrared gravitons screen Lambda?, Phys. Rev. D 77 (2008) 024021 [arXiv:0706.0295] [INSPIRE].
N.C. Tsamis and R.P. Woodard, Comment on ‘Can infrared gravitons screen Lambda?’, Phys. Rev. D 78 (2008) 028501 [arXiv:0708.2004] [INSPIRE].
A. Higuchi, D. Marolf and I.A. Morrison, de Sitter invariance of the dS graviton vacuum, Class. Quant. Grav. 28 (2011) 245012 [arXiv:1107.2712] [INSPIRE].
S.P. Miao, N.C. Tsamis and R.P. Woodard, Gauging away Physics, Class. Quant. Grav. 28 (2011) 245013 [arXiv:1107.4733] [INSPIRE].
I.A. Morrison, On cosmic hair and “de Sitter breaking” in linearized quantum gravity, arXiv:1302.1860 [INSPIRE].
S.P. Miao, P.J. Mora, N.C. Tsamis and R.P. Woodard, Perils of analytic continuation, Phys. Rev. D 89 (2014) 104004 [arXiv:1306.5410] [INSPIRE].
M.B. Fröb, The Weyl tensor correlator in cosmological spacetimes, JCAP 12 (2014) 010 [arXiv:1409.7964] [INSPIRE].
R.P. Woodard, Some Inconvenient Truths, JHEP 05 (2016) 152 [arXiv:1506.04252] [INSPIRE].
S. Park and R.P. Woodard, Scalar Contribution to the Graviton Self-Energy during Inflation, Phys. Rev. D 83 (2011) 084049 [arXiv:1101.5804] [INSPIRE].
S.P. Miao, T. Prokopec and R.P. Woodard, Deducing Cosmological Observables from the S-matrix, Phys. Rev. D 96 (2017) 104029 [arXiv:1708.06239] [INSPIRE].
J.F. Donoghue, Leading quantum correction to the Newtonian potential, Phys. Rev. Lett. 72 (1994) 2996 [gr-qc/9310024] [INSPIRE].
J.F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
J.F. Donoghue and T. Torma, On the power counting of loop diagrams in general relativity, Phys. Rev. D 54 (1996) 4963 [hep-th/9602121] [INSPIRE].
S. Katuwal and R.P. Woodard, Gauge independent quantum gravitational corrections to Maxwell’s equation, JHEP 21 (2020) 029 [arXiv:2107.13341] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, Graviton Propagator in a 2-Parameter Family of de Sitter Breaking Gauges, JHEP 10 (2019) 096 [arXiv:1908.06064] [INSPIRE].
N.C. Tsamis and R.P. Woodard, The Structure of perturbative quantum gravity on a de Sitter background, Commun. Math. Phys. 162 (1994) 217 [INSPIRE].
R.P. Woodard, de Sitter breaking in field theory, in Deserfest: A Celebration of the Life and Works of Stanley Deser, Ann Arbor U.S.A. (2004), pg. 339 [gr-qc/0408002] [INSPIRE].
V.K. Onemli and R.P. Woodard, Superacceleration from massless, minimally coupled ϕ4, Class. Quant. Grav. 19 (2002) 4607 [gr-qc/0204065] [INSPIRE].
V.K. Onemli and R.P. Woodard, Quantum effects can render w < −1 on cosmological scales, Phys. Rev. D 70 (2004) 107301 [gr-qc/0406098] [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
K.T. Mahanthappa, Multiple production of photons in quantum electrodynamics, Phys. Rev. 126 (1962) 329 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 1, J. Math. Phys. 4 (1963) 1 [INSPIRE].
P.M. Bakshi and K.T. Mahanthappa, Expectation value formalism in quantum field theory. 2, J. Math. Phys. 4 (1963) 12 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
K.C. Chou, Z.b. Su, B.l. Hao and L. Yu, Equilibrium and Nonequilibrium Formalisms Made Unified, Phys. Rept. 118 (1985) 1.
R.D. Jordan, Effective Field Equations for Expectation Values, Phys. Rev. D 33 (1986) 444 [INSPIRE].
E. Calzetta and B.L. Hu, Closed Time Path Functional Formalism in Curved Space-Time: Application to Cosmological Back Reaction Problems, Phys. Rev. D 35 (1987) 495 [INSPIRE].
L.H. Ford and R.P. Woodard, Stress tensor correlators in the Schwinger-Keldysh formalism, Class. Quant. Grav. 22 (2005) 1637 [gr-qc/0411003] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, Breaking of scaling symmetry by massless scalar on de Sitter, Phys. Lett. B 798 (2019) 134944 arXiv:1908.11113 [INSPIRE].
S.P. Miao, N.C. Tsamis and R.P. Woodard, Summing Inflationary Logarithms in Nonlinear Sigma Models, arXiv:2110.08715 [INSPIRE].
A.A. Starobinsky, Stochastic de Sitter (inflationary) stage in the early universe, Lect. Notes Phys. 246 (1986) 107 [INSPIRE].
A.A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background, Phys. Rev. D 50 (1994) 6357 [astro-ph/9407016] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge, Class. Quant. Grav. 32 (2015) 195014 [arXiv:1504.00894] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2112.00959
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Glavan, D., Miao, S.P., Prokopec, T. et al. Large logarithms from quantum gravitational corrections to a massless, minimally coupled scalar on de Sitter. J. High Energ. Phys. 2022, 88 (2022). https://doi.org/10.1007/JHEP03(2022)088
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)088