Abstract
We develop a novel framework for describing quantum fluctuations in field theory, with a focus on cosmological applications. Our method uniquely circumvents the use of operator/Hilbert-space formalism, instead relying on a systematic treatment of classical variables, quantum fluctuations, and an effective Hamiltonian. Our framework not only aligns with standard formalisms in flat and de Sitter spacetimes, which assumes no backreaction, demonstrated through the φ3-model, but also adeptly handles time-dependent backreaction in more general cases. The uncertainty principle and spatial symmetry emerge as critical tools for selecting initial conditions and understanding effective potentials. We discover that modes inside the Hubble horizon do not necessarily feel an initial Minkowski vacuum, as is commonly assumed. Our findings offer fresh insights into the early universe’s quantum fluctuations and potential explanations to large-scale CMB anomalies.
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References
M. Bojowald and A. Skirzewski, Effective equations of motion for quantum systems, Rev. Math. Phys. 18 (2006) 713 [math-ph/0511043] [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].
A.H. Guth, The Inflationary Universe: a Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rept. 215 (1992) 203 [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].
D. Krotov and A.M. Polyakov, Infrared Sensitivity of Unstable Vacua, Nucl. Phys. B 849 (2011) 410 [arXiv:1012.2107] [INSPIRE].
A.M. Polyakov, Infrared instability of the de Sitter space, arXiv:1209.4135 [INSPIRE].
U. Danielsson, The quantum swampland, JHEP 04 (2019) 095 [arXiv:1809.04512] [INSPIRE].
G. Jona-Lasinio, Relativistic field theories with symmetry breaking solutions, Nuovo Cim. 34 (1964) 1790 [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
R. Jackiw and A. Kerman, Time Dependent Variational Principle and the Effective Action, Phys. Lett. A 71 (1979) 158 [INSPIRE].
D.J. Mulryne, D. Seery and D. Wesley, Moment transport equations for non-Gaussianity, JCAP 01 (2010) 024 [arXiv:0909.2256] [INSPIRE].
D.J. Mulryne, D. Seery and D. Wesley, Moment transport equations for the primordial curvature perturbation, JCAP 04 (2011) 030 [arXiv:1008.3159] [INSPIRE].
T. Vachaspati and G. Zahariade, Classical-quantum correspondence and backreaction, Phys. Rev. D 98 (2018) 065002 [arXiv:1806.05196] [INSPIRE].
T. Vachaspati and G. Zahariade, Classical-Quantum Correspondence for Fields, JCAP 09 (2019) 015 [arXiv:1807.10282] [INSPIRE].
M. Bojowald and D. Ding, Canonical description of cosmological backreaction, JCAP 03 (2021) 083 [arXiv:2011.03018] [INSPIRE].
M. Bojowald et al., Multi-field inflation from single-field models, JCAP 08 (2021) 047 [arXiv:2011.02843] [INSPIRE].
M. Bojowald and S. Brahma, Canonical derivation of effective potentials, arXiv:1411.3636 [INSPIRE].
D. Brizuela and U. Muniain, A moment approach to compute quantum-gravity effects in the primordial universe, JCAP 04 (2019) 016 [arXiv:1901.08391] [INSPIRE].
D. Brizuela and I. de Leon, Mode coupling on a geometrodynamical quantization of an inflationary universe, JCAP 07 (2021) 054 [arXiv:2105.03138] [INSPIRE].
D. Brizuela and T. Pawlowski, Quantum fluctuations and semiclassicality in an inflaton-driven evolution, JCAP 10 (2022) 080 [arXiv:2107.04342] [INSPIRE].
J. Grain and V. Vennin, Canonical transformations and squeezing formalism in cosmology, JCAP 02 (2020) 022 [arXiv:1910.01916] [INSPIRE].
F. Arickx, J. Broeckhove, W. Coene and P. Van Leuven, Gaussian wave-packet dynamics, Int. J. Quant. Chem. 30 (1986) 471.
O.V. Prezhdo, Quantized Hamilton Dynamics, Theor. Chem. Acc. 116 (2005) 206.
M. Mukhopadhyay and T. Vachaspati, Rolling classical scalar field in a linear potential coupled to a quantum field, Phys. Rev. D 100 (2019) 096018 [arXiv:1907.03762] [INSPIRE].
T. Vachaspati and G. Zahariade, Classical-Quantum Correspondence and Hawking Radiation, JCAP 04 (2019) 013 [arXiv:1803.08919] [INSPIRE].
B. Baytaş, M. Bojowald and S. Crowe, Effective potentials from semiclassical truncations, Phys. Rev. A 99 (2019) 042114 [arXiv:1811.00505] [INSPIRE].
B. Baytas, M. Bojowald and S. Crowe, Faithful realizations of semiclassical truncations, Annals Phys. 420 (2020) 168247 [arXiv:1810.12127] [INSPIRE].
F. Cametti, G. Jona-Lasinio, C. Presilla and F. Toninelli, Comparison between quantum and classical dynamics in the effective action formalism, in the proceedings of the International School of Physics, ‘Enrico Fermi’, Course 143: New Directions in Quantum Chaos, Varenna, Italy, July 20–30 (1999) [https://doi.org/10.3254/978-1-61499-228-8-431] [quant-ph/9910065] [INSPIRE].
X. Chen, Primordial Non-Gaussianities from Inflation Models, Adv. Astron. 2010 (2010) 638979 [arXiv:1002.1416] [INSPIRE].
J. Martin and R.H. Brandenberger, The TransPlanckian problem of inflationary cosmology, Phys. Rev. D 63 (2001) 123501 [hep-th/0005209] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
S.A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7 (1973) 2850 [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
U.H. Danielsson, A note on inflation and transPlanckian physics, Phys. Rev. D 66 (2002) 023511 [hep-th/0203198] [INSPIRE].
C.J. Copi, D. Huterer, D.J. Schwarz and G.D. Starkman, Large angle anomalies in the CMB, Adv. Astron. 2010 (2010) 847541 [arXiv:1004.5602] [INSPIRE].
J. Garriga and V.F. Mukhanov, Perturbations in k-inflation, Phys. Lett. B 458 (1999) 219 [hep-th/9904176] [INSPIRE].
Acknowledgments
DD is supported by China Postdoctoral Science Foundation (Certificate No. 2023M730704). YW is supported by the General Program of Science and Technology of Shanghai No. 21ZR1406700, and Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01). YW is grateful for the Hospitality of the Perimeter Institute during his visit, where the main part of this work is done. We thank Martin Bojowald for discussions and useful suggestions.
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Ding, D., Zhao, Y. & Wan, Y. Effective dynamics of quantum fluctuations in field theory: with applications to cosmology. J. High Energ. Phys. 2024, 86 (2024). https://doi.org/10.1007/JHEP04(2024)086
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DOI: https://doi.org/10.1007/JHEP04(2024)086