Abstract
We define a perturbative S-matrix in a local patch of de Sitter background in the limit when the curvature length scale (ℓ) is large and study the ‘soft’ behavior of the scalar QED amplitudes in de Sitter spacetime in generic dimensions. We obtain the leading and subleading perturbative corrections to flat space soft photon theorems in the large ℓ limit, and comment on the universality of these corrections. We compare our results with the electromagnetic memory tails obtained earlier in d = 4 using classical radiation analysis.
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F. Bloch and A. Nordsieck, Note on the Radiation Field of the electron, Phys. Rev. 52 (1937) 54 [INSPIRE].
M. Gell-Mann and M.L. Goldberger, Scattering of low-energy photons by particles of spin 1/2, Phys. Rev. 96 (1954) 1433 [INSPIRE].
F.E. Low, Scattering of light of very low frequency by systems of spin 1/2, Phys. Rev. 96 (1954) 1428 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
D.J. Gross and R. Jackiw, Low-Energy Theorem for Graviton Scattering, Phys. Rev. 166 (1968) 1287 [INSPIRE].
R. Jackiw, Low-Energy Theorems for Massless Bosons: Photons and Gravitons, Phys. Rev. 168 (1968) 1623 [INSPIRE].
C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
R. Ferrari and L.E. Picasso, Spontaneous breakdown in quantum electrodynamics, Nucl. Phys. B 31 (1971) 316 [INSPIRE].
R. Ferrari and L.E. Picasso, Dynamical consequences of spontaneous breakdown of symmetries, Nucl. Phys. B 20 (1970) 553 [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New Symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [INSPIRE].
V. Lysov, S. Pasterski and A. Strominger, Low’s Subleading Soft Theorem as a Symmetry of QED, Phys. Rev. Lett. 113 (2014) 111601 [arXiv:1407.3814] [INSPIRE].
L. Susskind, Electromagnetic Memory, arXiv:1507.02584 [INSPIRE].
L. Bieri and D. Garfinkle, An electromagnetic analogue of gravitational wave memory, Class. Quant. Grav. 30 (2013) 195009 [arXiv:1307.5098] [INSPIRE].
S. Pasterski, Asymptotic Symmetries and Electromagnetic Memory, JHEP 09 (2017) 154 [arXiv:1505.00716] [INSPIRE].
A. Laddha and A. Sen, Gravity Waves from Soft Theorem in General Dimensions, JHEP 09 (2018) 105 [arXiv:1801.07719] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
P. Creminelli, J. Noreña and M. Simonović, Conformal consistency relations for single-field inflation, JCAP 07 (2012) 052 [arXiv:1203.4595] [INSPIRE].
V. Assassi, D. Baumann and D. Green, On Soft Limits of Inflationary Correlation Functions, JCAP 11 (2012) 047 [arXiv:1204.4207] [INSPIRE].
N. Kundu, A. Shukla and S.P. Trivedi, Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation, JHEP 04 (2015) 061 [arXiv:1410.2606] [INSPIRE].
A. Ghosh, N. Kundu, S. Raju and S.P. Trivedi, Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation, JHEP 07 (2014) 011 [arXiv:1401.1426] [INSPIRE].
C. Armstrong, A. Lipstein and J. Mei, Enhanced soft limits in de Sitter space, JHEP 12 (2022) 064 [arXiv:2210.02285] [INSPIRE].
L. Bieri, D. Garfinkle and S.-T. Yau, Gravitational wave memory in de Sitter spacetime, Phys. Rev. D 94 (2016) 064040 [arXiv:1509.01296] [INSPIRE].
Y.-Z. Chu, Gravitational Wave Memory In dS4+2n and 4D Cosmology, Class. Quant. Grav. 34 (2017) 035009 [arXiv:1603.00151] [INSPIRE].
A. Tolish and R.M. Wald, Cosmological memory effect, Phys. Rev. D 94 (2016) 044009 [arXiv:1606.04894] [INSPIRE].
Y. Hamada, M.-S. Seo and G. Shiu, Memory in de Sitter space and Bondi-Metzner-Sachs-like supertranslations, Phys. Rev. D 96 (2017) 023509 [arXiv:1702.06928] [INSPIRE].
M.A. Ismail, Y.-Z. Chu and Y.-W. Liu, Late time tails and nonlinear memories in asymptotically de Sitter spacetimes, Phys. Rev. D 104 (2021) 104038 [arXiv:2101.01736] [INSPIRE].
E. Albrychiewicz and Y. Neiman, Scattering in the static patch of de Sitter space, Phys. Rev. D 103 (2021) 065014 [arXiv:2012.13584] [INSPIRE].
S. Mandal and S. Banerjee, Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate, Eur. Phys. J. Plus 136 (2021) 1064 [arXiv:1908.06717] [INSPIRE].
D. Marolf, I.A. Morrison and M. Srednicki, Perturbative S-matrix for massive scalar fields in global de Sitter space, Class. Quant. Grav. 30 (2013) 155023 [arXiv:1209.6039] [INSPIRE].
R. Bousso, Cosmology and the S-matrix, Phys. Rev. D 71 (2005) 064024 [hep-th/0412197] [INSPIRE].
S. Atul Bhatkar, Effect of a small cosmological constant on the electromagnetic memory effect, Phys. Rev. D 105 (2022) 124028 [arXiv:2108.00835] [INSPIRE].
R. Aldrovandi and J.G. Pereira, An Introduction to Geometrical Physics, World Scientific (2016) [https://doi.org/10.1142/10202].
C.S.O. Mayor, De Sitter Relativity: foundations and some physical implications.
J. Bros and U. Moschella, Two point functions and quantum fields in de Sitter universe, Rev. Math. Phys. 8 (1996) 327 [gr-qc/9511019] [INSPIRE].
T.S. Bunch and L. Parker, Feynman Propagator in Curved Space-Time: A Momentum Space Representation, Phys. Rev. D 20 (1979) 2499 [INSPIRE].
T.S. Bunch, Local Momentum Space and Two Loop Renormalizability of λϕ4 Field Theory in Curved Space-time, Gen. Rel. Grav. 13 (1981) 711 [INSPIRE].
E. Poisson, A. Pound and I. Vega, The Motion of point particles in curved spacetime, Living Rev. Rel. 14 (2011) 7 [arXiv:1102.0529] [INSPIRE].
N. Banerjee, K. Fernandes and A. Mitra, 1/L2 corrected soft photon theorem from a CFT3 Ward identity, JHEP 04 (2023) 055 [arXiv:2209.06802] [INSPIRE].
N. Banerjee, K. Fernandes and A. Mitra, Soft photon theorem in the small negative cosmological constant limit, JHEP 08 (2021) 105 [arXiv:2102.06165] [INSPIRE].
Acknowledgments
We are extremely grateful to Alok Laddha and Ashoke Sen for numerous discussions and valuable suggestions during the project. We also thank Nabamita Banerjee, Abhijit Gadde, Shiraz Minwalla, Chintan Patel and Trakshu Sharma for discussions. We acknowledge the support of the Department of Atomic Energy, Government of India. SB is thankful for the support of the Infosys Endowment for the study of the Quantum Structure of Spacetime. Finally we would like to thank the people of India for their steady support for research in the basic sciences.
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Bhatkar, S., Jain, D. Perturbative soft photon theorems in de Sitter spacetime. J. High Energ. Phys. 2023, 55 (2023). https://doi.org/10.1007/JHEP10(2023)055
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DOI: https://doi.org/10.1007/JHEP10(2023)055