Abstract
We distinguish between the notions of asymptotic causality and infrared causality for gravitational effective field theories, and show that the latter gives constraints consistent with gravitational positivity bounds. We re-explore the scattering of gravitational waves in a spherically symmetric background in the EFT of gravity in D ≥ 5, for which the leading-order correction to Einstein gravity is determined by the Gauss-Bonnet operator. We reproduce the known result that the truncated effective theory exhibits apparent time advances relative to the background geometry for specific polarisations, which naively signal a violation of causality. We show that by properly identifying the regime of validity of the effective theory, the apparent time advance can be shown to be unresolvable. To illustrate this, we identify specific higher-dimension operators in the EFT expansion which become large for potentially resolvable time advances, rendering the EFT expansion invalid. Our results demonstrate how staying within the confines of the EFT, neither infrared nor asymptotic causality are ever violated for Einstein-Gauss-Bonnet gravity, no matter how low the scale, and furthermore its causality can be understood without appealing to a precise UV completion such as string theory.
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References
S.W. Hawking, The chronology protection conjecture, Phys. Rev. D 46 (1992) 603 [INSPIRE].
C. Burrage, C. de Rham, L. Heisenberg and A.J. Tolley, Chronology Protection in Galileon Models and Massive Gravity, JCAP 07 (2012) 004 [arXiv:1111.5549] [INSPIRE].
L. Eisenbud, The formal properties of nuclear collisions, Ph.D. Thesis, Princeton University, U.S.A. (1948).
E.P. Wigner, Lower Limit for the Energy Derivative of the Scattering Phase Shift, Phys. Rev. 98 (1955) 145 [INSPIRE].
F.T. Smith, Lifetime Matrix in Collision Theory, Phys. Rev. 118 (1960) 349 [INSPIRE].
P.A. Martin, On the Time Delay of Simple Scattering Systems, Commun. Math. Phys. 47 (1976) 221 [INSPIRE].
C.A. de Carvalho and H.M. Nussenzveig, Time delay, Phys. Rept. 364 (2002) 83.
H. Nussenzveig, Causality and dispersion relations, vol. 95, Academic Press, New York, London, (1972).
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
X.O. Camanho, G. Lucena Gómez and R. Rahman, Causality Constraints on Massive Gravity, Phys. Rev. D 96 (2017) 084007 [arXiv:1610.02033] [INSPIRE].
G. Goon and K. Hinterbichler, Superluminality, black holes and EFT, JHEP 02 (2017) 134 [arXiv:1609.00723] [INSPIRE].
K. Hinterbichler, A. Joyce and R.A. Rosen, Eikonal scattering and asymptotic superluminality of massless higher spin fields, Phys. Rev. D 97 (2018) 125019 [arXiv:1712.10021] [INSPIRE].
K. Hinterbichler, A. Joyce and R.A. Rosen, Massive Spin-2 Scattering and Asymptotic Superluminality, JHEP 03 (2018) 051 [arXiv:1708.05716] [INSPIRE].
M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini, Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity, Phys. Rev. D 102 (2020) 046014 [arXiv:2006.02375] [INSPIRE].
T.N. Pham and T.N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation, Phys. Rev. D 31 (1985) 3027 [INSPIRE].
B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints, Phys. Rev. D 51 (1995) 1093 [hep-ph/9410302] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
L.-Y. Chiang, Y.-t. Huang, W. Li, L. Rodina and H.-C. Weng, Into the EFThedron and UV constraints from IR consistency, arXiv:2105.02862 [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories, Phys. Rev. D 96 (2017) 081702 [arXiv:1702.06134] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, UV complete me: Positivity Bounds for Particles with Spin, JHEP 03 (2018) 011 [arXiv:1706.02712] [INSPIRE].
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive moments for scattering amplitudes, Phys. Rev. D 104 (2021) 036006 [arXiv:2011.00037] [INSPIRE].
A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry, JHEP 05 (2021) 255 [arXiv:2011.02400] [INSPIRE].
S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories, JHEP 05 (2021) 280 [arXiv:2011.02957] [INSPIRE].
A. Sinha and A. Zahed, Crossing Symmetric Dispersion Relations in Quantum Field Theories, Phys. Rev. Lett. 126 (2021) 181601 [arXiv:2012.04877] [INSPIRE].
Z.-Z. Du, C. Zhang and S.-Y. Zhou, Triple crossing positivity bounds for multi-field theories, JHEP 12 (2021) 115 [arXiv:2111.01169] [INSPIRE].
P. Haldar, A. Sinha and A. Zahed, Quantum field theory and the Bieberbach conjecture, SciPost Phys. 11 (2021) 002 [arXiv:2103.12108] [INSPIRE].
P. Raman and A. Sinha, QFT, EFT and GFT, JHEP 12 (2021) 203 [arXiv:2107.06559] [INSPIRE].
E. Babichev, V. Mukhanov and A. Vikman, k-Essence, superluminal propagation, causality and emergent geometry, JHEP 02 (2008) 101 [arXiv:0708.0561] [INSPIRE].
C. de Rham, Massive Gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
H.S. Reall, Causality in gravitational theories with second order equations of motion, Phys. Rev. D 103 (2021) 084027 [arXiv:2101.11623] [INSPIRE].
S. Gao and R.M. Wald, Theorems on gravitational time delay and related issues, Class. Quant. Grav. 17 (2000) 4999 [gr-qc/0007021] [INSPIRE].
C.Y.-R. Chen, C. de Rham, A. Margalit and A.J. Tolley, to appear.
C. de Rham and A.J. Tolley, Causality in curved spacetimes: The speed of light and gravity, Phys. Rev. D 102 (2020) 084048 [arXiv:2007.01847] [INSPIRE].
G. Papallo and H.S. Reall, Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory, JHEP 11 (2015) 109 [arXiv:1508.05303] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality Violation, Gravitational Shockwaves and UV Completion, JHEP 03 (2016) 129 [arXiv:1512.04952] [INSPIRE].
I.T. Drummond and S.J. Hathrell, QED Vacuum Polarization in a Background Gravitational Field and Its Effect on the Velocity of Photons, Phys. Rev. D 22 (1980) 343 [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality and Micro-Causality in Curved Spacetime, Phys. Lett. B 655 (2007) 67 [arXiv:0707.2302] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality, Renormalizability and Ultra-High Energy Gravitational Scattering, J. Phys. A 49 (2016) 215401 [arXiv:1601.06989] [INSPIRE].
G. D’Appollonio, P. Di Vecchia, R. Russo and G. Veneziano, Regge behavior saves String Theory from causality violations, JHEP 05 (2015) 144 [arXiv:1502.01254] [INSPIRE].
C. de Rham, A.J. Tolley and J. Zhang, Causality Constraints on Gravitational Effective Field Theories, arXiv:2112.05054 [INSPIRE].
C. de Rham and A.J. Tolley, Speed of gravity, Phys. Rev. D 101 (2020) 063518 [arXiv:1909.00881] [INSPIRE].
C. de Rham, J. Francfort and J. Zhang, Black Hole Gravitational Waves in the Effective Field Theory of Gravity, Phys. Rev. D 102 (2020) 024079 [arXiv:2005.13923] [INSPIRE].
H. Reall, N. Tanahashi and B. Way, Causality and Hyperbolicity of Lovelock Theories, Class. Quant. Grav. 31 (2014) 205005 [arXiv:1406.3379] [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, Positivity Bounds and the Massless Spin-2 Pole, Phys. Rev. D 102 (2020) 125023 [arXiv:2007.12667] [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, QED positivity bounds, Phys. Rev. D 103 (2021) 125020 [arXiv:2012.05798] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Sharp Boundaries for the Swampland, JHEP 07 (2021) 110 [arXiv:2102.08951] [INSPIRE].
Y. Hamada, T. Noumi and G. Shiu, Weak Gravity Conjecture from Unitarity and Causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
J. Tokuda, K. Aoki and S. Hirano, Gravitational positivity bounds, JHEP 11 (2020) 054 [arXiv:2007.15009] [INSPIRE].
M. Herrero-Valea, R. Santos-Garcia and A. Tokareva, Massless positivity in graviton exchange, Phys. Rev. D 104 (2021) 085022 [arXiv:2011.11652] [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, Reverse Bootstrapping: IR Lessons for UV Physics, Phys. Rev. Lett. 128 (2022) 051602 [arXiv:2111.09226] [INSPIRE].
B. Bellazzini, C. Cheung and G.N. Remmen, Quantum Gravity Constraints from Unitarity and Analyticity, Phys. Rev. D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].
C. Cheung and G.N. Remmen, Positivity of Curvature-Squared Corrections in Gravity, Phys. Rev. Lett. 118 (2017) 051601 [arXiv:1608.02942] [INSPIRE].
H. Kodama, A. Ishibashi and O. Seto, Brane world cosmology: Gauge invariant formalism for perturbation, Phys. Rev. D 62 (2000) 064022 [hep-th/0004160] [INSPIRE].
H. Kodama and A. Ishibashi, A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions, Prog. Theor. Phys. 110 (2003) 701 [hep-th/0305147] [INSPIRE].
A. Ishibashi and H. Kodama, Stability of higher dimensional Schwarzschild black holes, Prog. Theor. Phys. 110 (2003) 901 [hep-th/0305185] [INSPIRE].
T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108 (1957) 1063 [INSPIRE].
F.J. Zerilli, Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics, Phys. Rev. D 2 (1970) 2141 [INSPIRE].
G. Dotti and R.J. Gleiser, Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part I. Tensor perturbations, Phys. Rev. D 72 (2005) 044018 [gr-qc/0503117] [INSPIRE].
R.J. Gleiser and G. Dotti, Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part II: Vector and scalar perturbations, Phys. Rev. D 72 (2005) 124002 [gr-qc/0510069] [INSPIRE].
T. Takahashi and J. Soda, Stability of Lovelock Black Holes under Tensor Perturbations, Phys. Rev. D 79 (2009) 104025 [arXiv:0902.2921] [INSPIRE].
T. Takahashi and J. Soda, Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions, Prog. Theor. Phys. 124 (2010) 911 [arXiv:1008.1385] [INSPIRE].
K. Benakli, S. Chapman, L. Darmé and Y. Oz, Superluminal graviton propagation, Phys. Rev. D 94 (2016) 084026 [arXiv:1512.07245] [INSPIRE].
T. Andrade, E. Cáceres and C. Keeler, Boundary causality versus hyperbolicity for spherical black holes in Gauss-Bonnet gravity, Class. Quant. Grav. 34 (2017) 135003 [arXiv:1610.06078] [INSPIRE].
R. Brustein and Y. Sherf, Causality Violations in Lovelock Theories, Phys. Rev. D 97 (2018) 084019 [arXiv:1711.05140] [INSPIRE].
Y. Sherf, Hyperbolicity Constraints in Extended Gravity Theories, Phys. Scripta 94 (2019) 085005 [arXiv:1806.09984] [INSPIRE].
E. Cáceres, A.S. Misobuchi and J.F. Pedraza, Constraining higher order gravities with subregion duality, JHEP 11 (2019) 175 [arXiv:1907.08021] [INSPIRE].
D.J. Gross and E. Witten, Superstring Modifications of Einstein’s Equations, Nucl. Phys. B 277 (1986) 1 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Curvature Cubed Terms in String Theory Effective Actions, Phys. Lett. B 185 (1987) 52 [INSPIRE].
Z. Bern, D. Kosmopoulos and A. Zhiboedov, Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude, J. Phys. A 54 (2021) 344002 [arXiv:2103.12728] [INSPIRE].
G.L. Goon, K. Hinterbichler and M. Trodden, Stability and superluminality of spherical DBI galileon solutions, Phys. Rev. D 83 (2011) 085015 [arXiv:1008.4580] [INSPIRE].
P. de Fromont, C. de Rham, L. Heisenberg and A. Matas, Superluminality in the Bi- and Multi-Galileon, JHEP 07 (2013) 067 [arXiv:1303.0274] [INSPIRE].
C. de Rham, M. Fasiello and A.J. Tolley, Galileon Duality, Phys. Lett. B 733 (2014) 46 [arXiv:1308.2702] [INSPIRE].
L. Keltner and A.J. Tolley, UV properties of Galileons: Spectral Densities, arXiv:1502.05706 [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Massive Galileon Positivity Bounds, JHEP 09 (2017) 072 [arXiv:1702.08577] [INSPIRE].
J.D. Edelstein, G. Giribet, C. Gomez, E. Kilicarslan, M. Leoni and B. Tekin, Causality in 3D Massive Gravity Theories, Phys. Rev. D 95 (2017) 104016 [arXiv:1602.03376] [INSPIRE].
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, Shocks, Superconvergence, and a Stringy Equivalence Principle, JHEP 11 (2020) 096 [arXiv:1904.05905] [INSPIRE].
X.-H. Ge and S.-J. Sin, Causality of black holes in 4-dimensional Einstein-Gauss-Bonnet-Maxwell theory, Eur. Phys. J. C 80 (2020) 695 [arXiv:2004.12191] [INSPIRE].
J.D. Edelstein, R. Ghosh, A. Laddha and S. Sarkar, Causality constraints in Quadratic Gravity, JHEP 09 (2021) 150 [arXiv:2107.07424] [INSPIRE].
J.M. Martín-García et al., xAct: Efficient tensor computer algebra for Mathematica, http://xact.es/.
T. Nutma, xTras: A field-theory inspired xAct package for mathematica, Comput. Phys. Commun. 185 (2014) 1719 [arXiv:1308.3493] [INSPIRE].
A. Higuchi, Symmetric Tensor Spherical Harmonics on the N Sphere and Their Application to the de Sitter Group SO(N,1), J. Math. Phys. 28 (1987) 1553 [Erratum ibid. 43 (2002) 6385] [INSPIRE].
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Chen, C.YR., de Rham, C., Margalit, A. et al. A cautionary case of casual causality. J. High Energ. Phys. 2022, 25 (2022). https://doi.org/10.1007/JHEP03(2022)025
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DOI: https://doi.org/10.1007/JHEP03(2022)025