Positive signs in massive gravity

Cheung, Clifford; Remmen, Grant N.

doi:10.1007/JHEP04(2016)002

Title: Positive signs in massive gravity

Journal Article · Fri Apr 01 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP04(2016)002· OSTI ID:1327304

Cheung, Clifford ^[1]; Remmen, Grant N. ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Here, we derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphism-breaking corrections. We calculate scattering amplitudes for all combinations of tensor, vector, and scalar polarizations. Furthermore, the high-energy behavior of these amplitudes prescribes a specific choice of couplings that ameliorates the ultraviolet cutoff, in agreement with existing literature. We then derive consistency conditions from analytic dispersion relations, which dictate positivity of certain combinations of parameters appearing in the forward scattering amplitudes. These constraints exclude all but a small island in the parameter space of ghost-free massive gravity. And while the theory of the "Galileon" scalar mode alone is known to be inconsistent with positivity constraints, this is remedied in the full massive gravity theory.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0010255; DGE-1144469

OSTI ID:: 1327304

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 4; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 95 works

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References (20)

Theoretical aspects of massive gravity Hinterbichler, Kurt Reviews of Modern Physics, Vol. 84, Issue 2 https://doi.org/10.1103/RevModPhys.84.671	journal	May 2012
Effective field theory for massive gravitons and gravity in theory space Arkani-Hamed, Nima; Georgi, Howard; Schwartz, Matthew D. Annals of Physics, Vol. 305, Issue 2 https://doi.org/10.1016/S0003-4916(03)00068-X	journal	June 2003
Resummation of Massive Gravity de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J. Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.231101	journal	June 2011
Energy’s and amplitudes’ positivity Nicolis, Alberto; Rattazzi, Riccardo; Trincherini, Enrico Journal of High Energy Physics, Vol. 2010, Issue 5 https://doi.org/10.1007/JHEP05(2010)095	journal	May 2010
Causality, analyticity and an IR obstruction to UV completion Adams, Allan; Arkani-Hamed, Nima; Dubovsky, Sergei Journal of High Energy Physics, Vol. 2006, Issue 10 https://doi.org/10.1088/1126-6708/2006/10/014	journal	October 2006
Resolving the Ghost Problem in Nonlinear Massive Gravity Hassan, S. F.; Rosen, Rachel A. Physical Review Letters, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRevLett.108.041101	journal	January 2012
4D gravity on a brane in 5D Minkowski space Dvali, Gia; Gabadadze, Gregory; Porrati, Massimo Physics Letters B, Vol. 485, Issue 1-3 https://doi.org/10.1016/S0370-2693(00)00669-9	journal	July 2000
Strong interactions and stability in the DGP model Luty, Markus A.; Porrati, Massimo; Rattazzi, Riccardo Journal of High Energy Physics, Vol. 2003, Issue 09 https://doi.org/10.1088/1126-6708/2003/09/029	journal	September 2003
Asymptotic Behavior and Subtractions in the Mandelstam Representation Froissart, Marcel Physical Review, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRev.123.1053	journal	August 1961
Unitarity and High-Energy Behavior of Scattering Amplitudes Martin, A. Physical Review, Vol. 129, Issue 3 https://doi.org/10.1103/PhysRev.129.1432	journal	February 1963
NP-hardness of deciding convexity of quartic polynomials and related problems Ahmadi, Amir Ali; Olshevsky, Alex; Parrilo, Pablo A. Mathematical Programming, Vol. 137, Issue 1-2 https://doi.org/10.1007/s10107-011-0499-2	journal	November 2011
On the difficulty of deciding asymptotic stability of cubic homogeneous vector fields Ahmadi, A. A. 2012 American Control Conference - ACC 2012, 2012 American Control Conference (ACC) https://doi.org/10.1109/ACC.2012.6315687	conference	June 2012
Effective Field Theories from Soft Limits of Scattering Amplitudes Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 114, Issue 22 https://doi.org/10.1103/PhysRevLett.114.221602	journal	June 2015
Infrared consistency and the weak gravity conjecture Cheung, Clifford; Remmen, Grant N. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)087	journal	December 2014
Resummation of Massive Gravity de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J. arXiv https://doi.org/10.48550/arxiv.1011.1232	text	January 2010
NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems Ahmadi, Amir Ali; Olshevsky, Alex; Parrilo, Pablo A. arXiv https://doi.org/10.48550/arxiv.1012.1908	text	January 2010
Theoretical Aspects of Massive Gravity Hinterbichler, Kurt arXiv https://doi.org/10.48550/arxiv.1105.3735	text	January 2011
Resolving the Ghost Problem in non-Linear Massive Gravity Hassan, S. F.; Rosen, Rachel A. arXiv https://doi.org/10.48550/arxiv.1106.3344	text	January 2011
Infrared Consistency and the Weak Gravity Conjecture Cheung, Clifford; Remmen, Grant N. arXiv https://doi.org/10.48550/arxiv.1407.7865	text	January 2014
Causality, Analyticity and an IR Obstruction to UV Completion Adams, Allan; Arkani-Hamed, Nima; Dubovsky, Sergei arXiv https://doi.org/10.48550/arxiv.hep-th/0602178	text	January 2006

Cited By (12)

Slowly-rotating neutron stars in massive bigravity Sullivan, A.; Yunes, N. Classical and Quantum Gravity, Vol. 35, Issue 4 https://doi.org/10.1088/1361-6382/aaa3ab	journal	January 2018
Phenomenology in type-I minimally modified gravity Aoki, Katsuki; Felice, Antonio De; Lin, Chunshan Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 01 https://doi.org/10.1088/1475-7516/2019/01/017	journal	January 2019
Constraints on a gravitational Higgs mechanism Bonifacio, James; Hinterbichler, Kurt; Rosen, Rachel A. Physical Review D, Vol. 100, Issue 8 https://doi.org/10.1103/physrevd.100.084017	journal	October 2019
Spin-2 fields and the weak gravity conjecture de Rham, Claudia; Heisenberg, Lavinia; Tolley, Andrew J. Physical Review D, Vol. 100, Issue 10 https://doi.org/10.1103/physrevd.100.104033	journal	November 2019
Constraints on quasidilaton massive gravity Martinovic, Katarina; Sakellariadou, Mairi Physical Review D, Vol. 100, Issue 12 https://doi.org/10.1103/physrevd.100.124016	journal	December 2019
Bounds on amplitudes in effective theories with massive spinning particles Bonifacio, James; Hinterbichler, Kurt Physical Review D, Vol. 98, Issue 4 https://doi.org/10.1103/physrevd.98.045003	journal	August 2018
Spin-2 fields and the weak gravity conjecture Claudia, De Rha,; Lavinia, Heisenberg,; J., Tolley, Andrew ETH Zurich https://doi.org/10.3929/ethz-b-000381401	text	January 2019
Softness and Amplitudes' Positivity for Spinning Particles Bellazzini, Brando arXiv https://doi.org/10.48550/arxiv.1605.06111	text	January 2016
Slowly-Rotating Neutron Stars in Massive Bigravity Sullivan, Andrew; Yunes, Nicolas arXiv https://doi.org/10.48550/arxiv.1709.03311	text	January 2017
Phenomenology in type-I minimally modified gravity Aoki, Katsuki; De Felice, Antonio; Lin, Chunshan arXiv https://doi.org/10.48550/arxiv.1810.01047	text	January 2018
Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes Cheung, Clifford; Liu, Junyu; Remmen, Grant N. arXiv https://doi.org/10.48550/arxiv.1903.09156	text	January 2019
Sum Rules for Massive Spin-2 Kaluza-Klein Elastic Scattering Amplitudes Chivukula, R. Sekhar; Foren, Dennis; Mohan, Kirtimaan A. arXiv https://doi.org/10.48550/arxiv.1910.06159	text	January 2019

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