Abstract
Nonlinear sigma models on de Sitter background possess the same kind of derivative interactions as gravity, and show the same sorts of large spacetime logarithms in correlation functions and solutions to the effective field equations. It was recently demonstrated that these logarithms can be resummed by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. This work considers one of these models and completes two pieces of analysis which were left unfinished: the evolution of the background at two loop order and the one loop beta function.
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References
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
A.A. Starobinsky, Spectrum of relict gravitational radiation and the early state of the universe, JETP Lett. 30 (1979) 682 [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].
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 the proceedings of the Deserfest: A Celebration of the Life and Works of Stanley Deser, Ann Arbor, U.S.A., April 3–5 (2004), p. 339–351 [gr-qc/0408002] [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].
C.L. Wang and R.P. Woodard, Excitation of Photons by Inflationary Gravitons, Phys. Rev. D 91 (2015) 124054 [arXiv:1408.1448] [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].
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].
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].
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].
S.P. Miao and R.P. Woodard, Gravitons Enhance Fermions during Inflation, Phys. Rev. D 74 (2006) 024021 [gr-qc/0603135] [INSPIRE].
D. Glavan, S.P. Miao, T. Prokopec and R.P. Woodard, Large logarithms from quantum gravitational corrections to a massless, minimally coupled scalar on de Sitter, JHEP 03 (2022) 088 [arXiv:2112.00959] [INSPIRE].
L. Tan, N.C. Tsamis and R.P. Woodard, How inflationary gravitons affect gravitational radiation, Phil. Trans. Roy. Soc. Lond. A 380 (2021) 0187 [arXiv:2107.13905] [INSPIRE].
L. Tan, N.C. Tsamis and R.P. Woodard, How Inflationary Gravitons Affect the Force of Gravity, Universe 8 (2022) 376 [arXiv:2206.11467] [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].
R.P. Woodard, A Leading logarithm approximation for inflationary quantum field theory, Nucl. Phys. B Proc. Suppl. 148 (2005) 108 [astro-ph/0502556] [INSPIRE].
N.C. Tsamis and R.P. Woodard, Stochastic quantum gravitational inflation, Nucl. Phys. B 724 (2005) 295 [gr-qc/0505115] [INSPIRE].
S.-P. Miao and R.P. Woodard, A Simple Operator Check of the Effective Fermion Mode Function during Inflation, Class. Quant. Grav. 25 (2008) 145009 [arXiv:0803.2377] [INSPIRE].
R.P. Woodard, Cosmology is not a Renormalization Group Flow, Phys. Rev. Lett. 101 (2008) 081301 [arXiv:0805.3089] [INSPIRE].
C.P. Burgess, L. Leblond, R. Holman and S. Shandera, Super-Hubble de Sitter Fluctuations and the Dynamical RG, JCAP 03 (2010) 033 [arXiv:0912.1608] [INSPIRE].
C.P. Burgess, R. Holman, L. Leblond and S. Shandera, Breakdown of Semiclassical Methods in de Sitter Space, JCAP 10 (2010) 017 [arXiv:1005.3551] [INSPIRE].
C.P. Burgess, R. Holman and G. Tasinato, Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation, JHEP 01 (2016) 153 [arXiv:1512.00169] [INSPIRE].
H. Kitamoto and Y. Kitazawa, Non-linear sigma model in de Sitter space, Phys. Rev. D 83 (2011) 104043 [arXiv:1012.5930] [INSPIRE].
H. Kitamoto and Y. Kitazawa, Infra-red effects of Non-linear sigma model in de Sitter space, Phys. Rev. D 85 (2012) 044062 [arXiv:1109.4892] [INSPIRE].
H. Kitamoto, Infrared resummation for derivative interactions in de Sitter space, Phys. Rev. D 100 (2019) 025020 [arXiv:1811.01830] [INSPIRE].
S.P. Miao, N.C. Tsamis and R.P. Woodard, Summing inflationary logarithms in nonlinear sigma models, JHEP 03 (2022) 069 [arXiv:2110.08715] [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].
E. Kasdagli, M. Ulloa and R.P. Woodard, Coincident massless, minimally coupled scalar correlators on general cosmological backgrounds, Phys. Rev. D 107 (2023) 105023 [arXiv:2302.04808] [INSPIRE].
A.O. Barvinsky and G.A. Vilkovisky, The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
K.-C. Chou, Z.-B. Su, B.-L. Hao and L. Yu, Equilibrium and Nonequilibrium Formalisms Made Unified, Phys. Rept. 118 (1985) 1 [INSPIRE].
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].
Acknowledgments
We thank N. C. Tsamis for discussions on this topic. This work was partially supported by NSF grant PHY-2207514 and by the Institute for Fundamental Theory at the University of Florida.
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Woodard, R.P., Yesilyurt, B. Unfinished business in a nonlinear sigma model on de Sitter background. J. High Energ. Phys. 2023, 206 (2023). https://doi.org/10.1007/JHEP06(2023)206
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DOI: https://doi.org/10.1007/JHEP06(2023)206