Lorentz symmetry in ghost-free massive gravity

Kostelecký, V. Alan; Potting, Robertus

doi:10.1103/physrevd.104.104046

Title: Lorentz symmetry in ghost-free massive gravity

Journal Article · Wed Nov 17 00:00:00 EST 2021 · Physical Review. D.

DOI:https://doi.org/10.1103/physrevd.104.104046· OSTI ID:1843789

^[1];

^[2]

Indiana Univ., Bloomington, IN (United States)
University of Algarve, Faro (Portugal); Univ. of Lisbon (Portugal)

The role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. Here, the result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Indiana Univ., Bloomington, IN (United States)

Sponsoring Organization:: USDOE; Portuguese Fundação para a Ciência e a Tecnologia; Indiana University

Grant/Contract Number:: SC0010120; SFRH/BSAB/150324/2019; UID/FIS/00099/2019

OSTI ID:: 1843789

Journal Information:: Physical Review. D., Vol. 104, Issue 10; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (60)

Superluminality in the Bi- and Multi-Galileon de Fromont, Paul; de Rham, Claudia; Heisenberg, Lavinia Journal of High Energy Physics, Vol. 2013, Issue 7 https://doi.org/10.1007/JHEP07(2013)067	journal	July 2013
Searches for beyond-Riemann gravity Kostelecký, V. Alan; Li, Zonghao Physical Review D, Vol. 104, Issue 4 https://doi.org/10.1103/PhysRevD.104.044054	journal	August 2021
Photon and graviton mass limits Goldhaber, Alfred Scharff; Nieto, Michael Martin Reviews of Modern Physics, Vol. 82, Issue 1 https://doi.org/10.1103/RevModPhys.82.939	journal	March 2010
Ghost free massive gravity in the Stückelberg language de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J. Physics Letters B, Vol. 711, Issue 2 https://doi.org/10.1016/j.physletb.2012.03.081	journal	May 2012
To the problem of nonvanishing gravitation mass Vainshtein, A. I. Physics Letters B, Vol. 39, Issue 3 https://doi.org/10.1016/0370-2693(72)90147-5	journal	May 1972
Classical kinematics for Lorentz violation Kostelecký, V. Alan; Russell, Neil Physics Letters B, Vol. 693, Issue 4 https://doi.org/10.1016/j.physletb.2010.08.069	journal	October 2010
Gravity from local Lorentz violation Kostelecký, V. Alan; Potting, Robertus General Relativity and Gravitation, Vol. 37, Issue 10 https://doi.org/10.1007/s10714-005-0149-1	journal	October 2005
Ghost-free massive gravity with a general reference metric Hassan, S. F.; Rosen, Rachel A.; Schmidt-May, Angnis Journal of High Energy Physics, Vol. 2012, Issue 2 https://doi.org/10.1007/JHEP02(2012)026	journal	February 2012
Canonical structure of tetrad bimetric gravity Alexandrov, Sergei General Relativity and Gravitation, Vol. 46, Issue 1 https://doi.org/10.1007/s10714-013-1639-1	journal	December 2013
Special-Relativistic Derivation of Generally Covariant Gravitation Theory Kraichnan, Robert H. Physical Review, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRev.98.1118	journal	May 1955
On non-linear actions for massive gravity Hassan, S. F.; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/JHEP07(2011)009	journal	July 2011
Data tables for Lorentz and $C P T$ violation Kostelecký, V. Alan; Russell, Neil Reviews of Modern Physics, Vol. 83, Issue 1 https://doi.org/10.1103/RevModPhys.83.11	journal	March 2011
Stability, causality, and Lorentz and $CPT$ violation Kostelecký, V. Alan; Lehnert, Ralf Physical Review D, Vol. 63, Issue 6 https://doi.org/10.1103/PhysRevD.63.065008	journal	February 2001
Massive and mass-less Yang-Mills and gravitational fields van Dam, H.; Veltman, M. Nuclear Physics B, Vol. 22, Issue 2 https://doi.org/10.1016/0550-3213(70)90416-5	journal	September 1970
Backgrounds in gravitational effective field theory Kostelecký, V. Alan; Li, Zonghao Physical Review D, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevD.103.024059	journal	January 2021
Zum Problem der Anaphylaxie mit chemisch bekannten Substanzen Fierz-David, Hans Eduard; Jadassohn, Werner; Kleemann, Alois Helvetica Chimica Acta, Vol. 22, Issue 1 https://doi.org/10.1002/hlca.19390220102	journal	January 1939
Gravitation and Electromagnetism Gupta, Suraj N. Physical Review, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRev.96.1683	journal	December 1954
Gravity, Lorentz violation, and the standard model Kostelecký, V. Alan Physical Review D, Vol. 69, Issue 10 https://doi.org/10.1103/PhysRevD.69.105009	journal	May 2004
Riemann–Finsler geometry and Lorentz-violating kinematics Kostelecký, V. Alan Physics Letters B, Vol. 701, Issue 1 https://doi.org/10.1016/j.physletb.2011.05.041	journal	June 2011
Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity Bluhm, Robert; Fung, Shu-Hong; Kostelecký, V. Alan Physical Review D, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevD.77.065020	journal	March 2008
Photons and Gravitons in Perturbation Theory: Derivation of Maxwell's and Einstein's Equations Weinberg, Steven Physical Review, Vol. 138, Issue 4B https://doi.org/10.1103/PhysRev.138.B988	journal	May 1965
Lorentz-violating gravity and the bootstrap procedure Seifert, Michael D. Classical and Quantum Gravity, Vol. 37, Issue 6 https://doi.org/10.1088/1361-6382/ab53ef	journal	February 2020
Self-interaction and gauge invariance Deser, S. General Relativity and Gravitation, Vol. 1, Issue 1 https://doi.org/10.1007/BF00759198	journal	January 1970
Dynamical Structure and Definition of Energy in General Relativity Arnowitt, R.; Deser, S.; Misner, C. W. Physical Review, Vol. 116, Issue 5 https://doi.org/10.1103/PhysRev.116.1322	journal	December 1959
Lorentz and diffeomorphism violations in linearized gravity Kostelecký, V. Alan; Mewes, Matthew Physics Letters B, Vol. 779 https://doi.org/10.1016/j.physletb.2018.01.082	journal	April 2018
Can Gravitation Have a Finite Range? Boulware, David G.; Deser, S. Physical Review D, Vol. 6, Issue 12 https://doi.org/10.1103/PhysRevD.6.3368	journal	December 1972
Signals for Lorentz violation in electrodynamics Kostelecký, V. Alan; Mewes, Matthew Physical Review D, Vol. 66, Issue 5 https://doi.org/10.1103/PhysRevD.66.056005	journal	September 2002
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
Classical general relativity derived from quantum gravity Boulware, David G.; Deser, S. Annals of Physics, Vol. 89, Issue 1 https://doi.org/10.1016/0003-4916(75)90302-4	journal	January 1975
Axial Vector Current Conservation in Weak Interactions Nambu, Yoichiro Physical Review Letters, Vol. 4, Issue 7 https://doi.org/10.1103/PhysRevLett.4.380	journal	April 1960
Quantization of Einstein's Gravitational Field: General Treatment Gupta, Suraj N. Proceedings of the Physical Society. Section A, Vol. 65, Issue 8 https://doi.org/10.1088/0370-1298/65/8/304	journal	August 1952
Massive gravity acausality redux Deser, S.; Izumi, K.; Ong, Y. C. Physics Letters B, Vol. 726, Issue 1-3 https://doi.org/10.1016/j.physletb.2013.09.001	journal	October 2013
Gravity from self-interaction in a curved background Deser, S. Classical and Quantum Gravity, Vol. 4, Issue 4 https://doi.org/10.1088/0264-9381/4/4/006	journal	July 1987
Short-range gravity and Lorentz violation Bailey, Quentin G.; Kostelecký, V. Alan; Xu, Rui Physical Review D, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevD.91.022006	journal	January 2015
Gravity with Explicit Diffeomorphism Breaking Bluhm, Robert; Yang, Yumu Symmetry, Vol. 13, Issue 4 https://doi.org/10.3390/sym13040660	journal	April 2021
Combined Search for Lorentz Violation in Short-Range Gravity Shao, Cheng-Gang; Tan, Yu-Jie; Tan, Wen-Hai Physical Review Letters, Vol. 117, Issue 7 https://doi.org/10.1103/PhysRevLett.117.071102	journal	August 2016
Interacting spin-2 fields Hinterbichler, Kurt; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)047	journal	July 2012
Riemann–Finsler geometry and Lorentz-violating scalar fields Edwards, Benjamin R.; Kostelecký, V. Alan Physics Letters B, Vol. 786 https://doi.org/10.1016/j.physletb.2018.10.011	journal	November 2018
Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity Hassan, S. F.; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2012, Issue 4 https://doi.org/10.1007/JHEP04(2012)123	journal	April 2012
Signals for Lorentz violation in post-Newtonian gravity Bailey, Quentin G.; Kostelecký, V. Alan Physical Review D, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevD.74.045001	journal	August 2006
Massive Gravity de Rham, Claudia Living Reviews in Relativity, Vol. 17, Issue 1 https://doi.org/10.12942/lrr-2014-7	journal	August 2014
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
An alternative approach to the theory of gravitation Thirring, Walter E. Annals of Physics, Vol. 16, Issue 1 https://doi.org/10.1016/0003-4916(61)90182-8	journal	October 1961
Gravity from spontaneous Lorentz violation Kostelecký, V. Alan; Potting, Robertus Physical Review D, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevD.79.065018	journal	March 2009
Testing local Lorentz invariance with short-range gravity Kostelecký, V. Alan; Mewes, Matthew Physics Letters B, Vol. 766 https://doi.org/10.1016/j.physletb.2016.12.062	journal	March 2017
Einstein's and Other Theories of Gravitation Gupta, Suraj N. Reviews of Modern Physics, Vol. 29, Issue 3 https://doi.org/10.1103/RevModPhys.29.334	journal	July 1957
Bimetric gravity from ghost-free massive gravity Hassan, S. F.; Rosen, Rachel A. Journal of High Energy Physics, Vol. 2012, Issue 2 https://doi.org/10.1007/JHEP02(2012)126	journal	February 2012
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
Electrodynamics with Lorentz-violating operators of arbitrary dimension Kostelecký, V. Alan; Mewes, Matthew Physical Review D, Vol. 80, Issue 1 https://doi.org/10.1103/PhysRevD.80.015020	journal	July 2009
Broken Symmetries Goldstone, Jeffrey; Salam, Abdus; Weinberg, Steven Physical Review, Vol. 127, Issue 3 https://doi.org/10.1103/PhysRev.127.965	journal	August 1962
$CPT$ violation and the standard model Colladay, Don; Kostelecký, V. Alan Physical Review D, Vol. 55, Issue 11 https://doi.org/10.1103/PhysRevD.55.6760	journal	June 1997
Supergravity from self-interaction Boulware, D. G.; Deser, S.; Kay, J. H. Physica A: Statistical Mechanics and its Applications, Vol. 96, Issue 1-2 https://doi.org/10.1016/0378-4371(79)90202-4	journal	April 1979
Lorentz-violating extension of the standard model Colladay, D.; Kostelecký, V. Alan Physical Review D, Vol. 58, Issue 11 https://doi.org/10.1103/PhysRevD.58.116002	journal	October 1998
Recent developments in bimetric theory Schmidt-May, Angnis; Strauss, Mikael von Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 18 https://doi.org/10.1088/1751-8113/49/18/183001	journal	March 2016
Matter-gravity couplings and Lorentz violation Kostelecký, V. Alan; Tasson, Jay D. Physical Review D, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevD.83.016013	journal	January 2011
Acausality of Massive Gravity Deser, S.; Waldron, A. Physical Review Letters, Vol. 110, Issue 11 https://doi.org/10.1103/PhysRevLett.110.111101	journal	March 2013
Lorentz violation in Goldstone gravity Carroll, Sean M.; Tam, Heywood; Wehus, Ingunn Kathrine Physical Review D, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevD.80.025020	journal	July 2009
Combined Search for a Lorentz-Violating Force in Short-Range Gravity Varying as the Inverse Sixth Power of Distance Shao, Cheng-Gang; Chen, Ya-Fen; Tan, Yu-Jie Physical Review Letters, Vol. 122, Issue 1 https://doi.org/10.1103/PhysRevLett.122.011102	journal	January 2019
Spontaneous Lorentz violation, Nambu-Goldstone modes, and gravity Bluhm, Robert; Kostelecký, V. Alan Physical Review D, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevD.71.065008	journal	March 2005
Nonlinear partially massless from massive gravity? Deser, S.; Sandora, M.; Waldron, A. Physical Review D, Vol. 87, Issue 10 https://doi.org/10.1103/PhysRevD.87.101501	journal	May 2013

Similar Records

Bigravity and Lorentz-violating massive gravity

Journal Article · Thu Nov 15 00:00:00 EST 2007 · Physical Review. D, Particles Fields · OSTI ID:1843789

Blas, D; Garriga, J; Deffayet, C

Lorentz violation in Goldstone gravity

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Physical Review. D, Particles Fields · OSTI ID:1843789

Carroll, Sean M; Tam, Heywood; Wehus, Ingunn Kathrine

Tuning the cosmological constant, broken scale invariance, unitarity

Journal Article · Fri Jun 10 00:00:00 EDT 2016 · Journal of Cosmology and Astroparticle Physics · OSTI ID:1843789

Förste, Stefan; Manz, Paul

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
Alternative gravity theories
General relativity
Gravitation

Title: Lorentz symmetry in ghost-free massive gravity

Citation Formats

References (60)

Similar Records

Related Subjects