Tests of Lorentz Symmetry in the Gravitational Sector

Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz symmetry. This review focuses on Lorentz symmetry tests performed in the gravitational sector. We briefly review the basics of the pure gravitational sector of the Standard-Model Extension (SME) framework, a formalism developed in order to systematically parametrize hypothetical violations of the Lorentz invariance. Furthermore, we discuss the latest constraints obtained within this formalism including analyses of the following measurements: atomic gravimetry, Lunar Laser Ranging, Very Long Baseline Interferometry, planetary ephemerides, Gravity Probe B, binary pulsars, high energy cosmic rays, … In addition, we propose a combined analysis of all these results. We also discuss possible improvements on current analyses and present some sensitivity analyses for future observations.

[1]  V. Kostelecký,et al.  CPT and strings , 1991 .

[2]  Y. Bonder.  Lorentz violation in the gravity sector: The t puzzle , 2015, 1504.03636.

[3]  Kazuhiro Yamamoto,et al.  Constraint on modified dispersion relations for gravitational waves from gravitational Cherenkov radiation , 2015, 1509.00610.

[4]  S. Reynaud,et al.  Post-Einsteinian tests of linearized gravitation , 2005, gr-qc/0502007.

[5]  D. Lorimer.  Binary and Millisecond Pulsars , 1998, Living reviews in relativity.

[6]  A. Kostelecký,et al.  Signals for Lorentz violation in post-Newtonian gravity , 2006, gr-qc/0603030.

[7]  Quentin G. Bailey,et al.  Light-bending tests of Lorentz invariance , 2011, 1108.2071.

[8]  Towards a 1% measurement of the Lense-Thirring effect with LARES? , 2008, 0802.2031.

[9]  J. Tasson,et al.  Matter-Sector Lorentz Violation in Binary Pulsars , 2015, 1510.03798.

[10]  D. Budker,et al.  Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium. , 2013, Physical review letters.

[11]  S. Ransom,et al.  HIGH-PRECISION TIMING OF FIVE MILLISECOND PULSARS: SPACE VELOCITIES, BINARY EVOLUTION, AND EQUIVALENCE PRINCIPLES , 2011, 1109.5638.

[12]  E. C. Pavlis,et al.  A confirmation of the general relativistic prediction of the Lense–Thirring effect , 2004, Nature.

[13]  A. Fienga,et al.  INPOP08, a 4-D planetary ephemeris: from asteroid and time-scale computations to ESA Mars Express and Venus Express contributions , 2009, 0906.2860.

[14]  C. Le Poncin-Lafitte,et al.  Relativistic formulation of coordinate light time, Doppler and astrometric observables up to the second post-Minkowskian order , 2014, 1401.7622.

[15]  P. K. Seidelmann,et al.  The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement , 2003, astro-ph/0303376.

[16]  A. Peters,et al.  First gravity measurements using the mobile atom interferometer GAIN , 2013 .

[17]  L. Shao,et al.  Tests of local Lorentz invariance violation of gravity in the standard model extension with pulsars. , 2014, Physical review letters.

[18]  J. Ulrichs,et al.  The cosmic-ray energy spectrum above 1017 eV , 1986 .

[19]  Kazuhiro Yamamoto,et al.  Constraints on general second-order scalar-tensor models from gravitational Cherenkov radiation , 2011, 1112.4284.

[20]  Robert C Myers,et al.  Ultraviolet modifications of dispersion relations in effective field theory. , 2003, Physical review letters.

[21]  B. Famaey,et al.  Combined Solar system and rotation curve constraints on MOND , 2015, 1510.01369.

[22]  David Mattingly,et al.  Modern Tests of Lorentz Invariance , 2005, Living reviews in relativity.

[23]  E. Pitjeva,et al.  Relativistic effects and dark matter in the Solar system from observations of planets and spacecraft , 2013, 1306.3043.

[24]  L. Iorio.  Orbital effects of Lorentz-violating standard model extension gravitomagnetism around a static body: a sensitivity analysis , 2012, 1203.1859.

[25]  Sami W. Asmar,et al.  High‐resolution lunar gravity fields from the GRAIL Primary and Extended Missions , 2014 .

[26]  G. Moore,et al.  Constraining the New Aether: gravitational Cherenkov radiation , 2005, hep-ph/0505211.

[27]  W. Folkner,et al.  The Planetary and Lunar Ephemeris DE 421 , 2009 .

[28]  Long range gravity tests and the Pioneer anomaly , 2006, gr-qc/0610160.

[29]  P. G. Isar,et al.  SEARCHES FOR ANISOTROPIES IN THE ARRIVAL DIRECTIONS OF THE HIGHEST ENERGY COSMIC RAYS DETECTED BY THE PIERRE AUGER OBSERVATORY , 2015 .

[30]  Kenneth Nordtvedt,et al.  EQUIVALENCE PRINCIPLE FOR MASSIVE BODIES. II. THEORY. , 1968 .

[31]  A. Fienga,et al.  Gravity tests with INPOP planetary ephemerides , 2009, Proceedings of the International Astronomical Union.

[32]  Roberto Peron,et al.  Accurate measurement in the field of the earth of the general-relativistic precession of the LAGEOS II pericenter and new constraints on non-newtonian gravity. , 2010, Physical review letters.

[33]  H. Müller,et al.  Equivalence principle and gravitational redshift. , 2011, Physical review letters.

[34]  Cosmology and the standard model , 2002, hep-th/0210202.

[35]  L. Mervart,et al.  Status of GRAIL Gravity Field Determination Using the Celestial Mechanics Approach , 2014 .

[36]  N. Wex.  Testing Relativistic Gravity with Radio Pulsars , 2014, 1402.5594.

[37]  James G. Williams,et al.  Progress in lunar laser ranging tests of relativistic gravity. , 2006, Physical review letters.

[38]  P. M. Bell.  The search for non‐Newtonian G , 1981 .

[39]  Slava G. Turyshev,et al.  LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON , 2005 .

[40]  P. Tortora,et al.  A test of general relativity using radio links with the Cassini spacecraft , 2003, Nature.

[41]  J. W. Elbert,et al.  Detection of a Cosmic Ray with Measured Energy Well beyond the Expected Spectral Cutoff due to Cosmic Microwave Radiation , 1994 .

[42]  S. Lambert,et al.  Improved determination of γ by VLBI , 2011 .

[43]  T. Damour,et al.  Nonperturbative strong-field effects in tensor-scalar theories of gravitation. , 1993, Physical review letters.

[44]  Q. Bailey.  Time delay and Doppler tests of the Lorentz symmetry of gravity , 2009, 0904.0278.

[45]  George E. Pugh,et al.  PROPOSAL FOR A SATELLITE TEST OF THE CORIOLIS PREDICTIONS OF GENERAL RELATIVITY , 2003 .

[46]  J. H. J. de Bruijne,et al.  Science performance of Gaia, ESA’s space-astrometry mission , 2012, 1201.3238.

[47]  M. Zuber,et al.  Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters , 2011 .

[48]  R. N. Manchester,et al.  Tests of General Relativity from Timing the Double Pulsar , 2006, Science.

[49]  A. Bennett,et al.  TOPEX/POSEIDON tides estimated using a global inverse model , 1994 .

[50]  F. Pretorius,et al.  Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226 , 2016, 1603.08955.

[51]  N. Yunes,et al.  Constraints on Einstein-Æther theory and Hořava gravity from binary pulsar observations , 2013, 1311.7144.

[52]  M.Hayakawa.  Perturbative analysis on infrared aspects of noncommutative QED on R^4 , 1999, hep-th/9912094.

[53]  Sébastien Merlet,et al.  Micro-gravity investigations for the LNE watt balance project , 2008 .

[54]  Alan Kostelecky,et al.  Lorentz-Violating Extension of the Standard Model , 1998 .

[55]  C. Hernaski.  Quantization and stability of bumblebee electrodynamics , 2014, 1411.5321.

[56]  V. Skavysh,et al.  SEARCH FOR LORENTZ VIOLATION IN A SHORT-RANGE GRAVITY EXPERIMENT , 2010, 1008.3670.

[57]  C. Salomon,et al.  Atomic clock ensemble in space , 2011 .

[58]  J. Tasson,et al.  Constraints on torsion from bounds on lorentz violation. , 2007, Physical review letters.

[59]  G. Amelino-Camelia.  Quantum-Spacetime Phenomenology , 2008, Living reviews in relativity.

[60]  S. Reynaud,et al.  Radioscience simulations in general relativity and in alternative theories of gravity , 2011, 1105.5927.

[61]  Samuel,et al.  Spontaneous breaking of Lorentz symmetry in string theory. , 1989, Physical review. D, Particles and fields.

[62]  Pierre Touboul,et al.  The MICROSCOPE experiment, ready for the in-orbit test of the equivalence principle , 2012 .

[63]  A. Fienga,et al.  INPOP06: a new numerical planetary ephemeris , 2008 .

[64]  E. Standish,et al.  CHAPTER 8 : Orbital Ephemerides of the Sun , Moon , and Planets , 2007 .

[65]  T. Damour,et al.  General relativistic celestial mechanics of binary systems. II. The post-newtonian timing formula , 1986 .

[66]  M. Hayakawa.  Perturbative analysis on infrared aspects of noncommutative QED on R4 , 2000 .

[67]  R. Manchester,et al.  tempo2, a new pulsar timing package ¿ II. The timing model and precision estimates , 2006, astro-ph/0607664.

[68]  Zhongkun Hu,et al.  Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter , 2013 .

[69]  Clifford M. Will,et al.  The Confrontation between General Relativity and Experiment , 2001, Living reviews in relativity.

[70]  Fischbach,et al.  Reanalysis of the Eoumltvös experiment. , 1986, Physical review letters.

[71]  R. Warburton,et al.  Search for evidence of a preferred reference frame. [gravitational anisotropic effect on earth tides] , 1976 .

[72]  E. Adelberger,et al.  Preferred-Frame and CP-Violation Tests with Polarized Electrons , 2007, 0808.2673.

[73]  A. Kostelecký,et al.  Signals for Lorentz violation in electrodynamics , 2002, hep-ph/0205211.

[74]  Leonard I. Schiff,et al.  Possible New Experimental Test of General Relativity Theory , 1960 .

[75]  J. Williams,et al.  Lunar Laser Ranging: A Continuing Legacy of the Apollo Program , 1994, Science.

[76]  J. H. Taylor,et al.  Measurements of general relativistic effects in the binary pulsar PSR1913 + 16 , 1979, Nature.

[77]  M. Kramer,et al.  A characteristic observable signature of preferred-frame effects in relativistic binary pulsars , 2007, 0706.2382.

[78]  K. Thorne,et al.  Theoretical frameworks for testing relativistic gravity: A review , 1971 .

[79]  K. Nordtvedt.  Equivalence Principle for Massive Bodies. I. Phenomenology , 1968 .

[80]  P. Wolf,et al.  Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6 , 2015, 1508.06159.

[81]  S. Asmar,et al.  PROBING SPACE–TIME IN THE SOLAR SYSTEM: FROM CASSINI TO BEPICOLOMBO , 2007 .

[82]  World function and time transfer: general post-Minkowskian expansions , 2004, gr-qc/0403094.

[83]  George F. Smoot,et al.  A Brief History of Gravitational Waves , 2016 .

[84]  Marc-Thierry Jaekel,et al.  GRAVITY TESTS IN THE SOLAR SYSTEM AND THE PIONEER ANOMALY , 2004 .

[85]  E. Pitjeva.  High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants , 2005 .

[86]  J. Overduin,et al.  Limits on violations of Lorentz symmetry from Gravity Probe B , 2013, 1309.6399.

[87]  S. Chiow,et al.  Atom interferometry tests of local Lorentz invariance in gravity and electrodynamics , 2009, 0905.1929.

[88]  S. Bertone,et al.  Light propagation in the field of a moving axisymmetric body: Theory and applications to the Juno mission , 2014, 1406.6600.

[89]  K. Nordtvedt.  Anisotropic parametrized post-Newtonian gravitational metric field , 1976 .

[90]  Lorenzo Iorio,et al.  An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging , 2008, 0809.1373.

[91]  Slava G. Turyshev,et al.  Experimental tests of general relativity: recent progress and future directions , 2008, 0806.1731.

[92]  The Ligo Scientific Collaboration,et al.  Observation of Gravitational Waves from a Binary Black Hole Merger , 2016, 1602.03837.

[93]  String theoretic bounds on Lorentz violating warped compactification , 2003, hep-th/0301189.

[94]  N. Wex,et al.  New tests of local Lorentz invariance of gravity with small-eccentricity binary pulsars , 2012, 1209.4503.

[95]  Mario Vietri,et al.  KHZ QUASIPERIODIC OSCILLATIONS IN LOW-MASS X-RAY BINARIES AS PROBES OF GENERAL RELATIVITY IN THE STRONG-FIELD REGIME , 1998 .

[96]  CPT Violation and decoherence in quantum gravity , 2009, 0904.0606.

[97]  S. Reynaud,et al.  Simulations of Solar System Observations in Alternative Theories of Gravity , 2013, 1301.1658.

[98]  R. Hulse,et al.  Further observations of the binary pulsar PSR 1913+16. , 1976 .

[99]  Marco O. P. Sampaio,et al.  Testing general relativity with present and future astrophysical observations , 2015, 1501.07274.

[100]  A. Kostelecký,et al.  Short-Range Gravity and Lorentz Violation , 2014, 1410.6162.

[101]  A. Kostelecký,et al.  Lorentz Violation with an Antisymmetric Tensor , 2009, 0912.4852.

[102]  Q. Bailey.  Lorentz-violating gravitoelectromagnetism , 2010, 1005.1435.

[103]  E. F. Arias,et al.  THE SECOND REALIZATION OF THE INTERNATIONAL CELESTIAL REFERENCE FRAME BY VERY LONG BASELINE INTERFEROMETRY , 2015 .

[104]  E. V. Pitjeva,et al.  Development of planetary ephemerides EPM and their applications , 2014 .

[105]  R. Hulse,et al.  Discovery of a pulsar in a binary system , 1975 .

[106]  C. Talmadge.  Reanalysis of the Eotvos Experiment , 1987 .

[107]  Tensor-scalar gravity and binary-pulsar experiments. , 1996, Physical review. D, Particles and fields.

[108]  C. Le Poncin-Lafitte,et al.  General post-Minkowskian expansion of time transfer functions , 2008, 0803.0277.

[109]  A. Balakin,et al.  Einstein-aether theory with a Maxwell field: General formalism , 2014, 1407.6014.

[110]  M. Planck,et al.  The Confrontation between General Relativity and Experiment , 2006 .

[111]  A. Fienga,et al.  Numerical estimation of the sensitivity of INPOP planetary ephemerides to general relativity parameters , 2015 .

[112]  T. Damour,et al.  Strong-field tests of relativistic gravity and binary pulsars. , 1991, Physical review. D, Particles and fields.

[113]  E. Pitjeva.  Updated IAA RAS planetary ephemerides-EPM2011 and their use in scientific research , 2013, 1308.6416.

[114]  R. Penrose,et al.  A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model , 2016, The European physical journal. C, Particles and fields.

[115]  G. Renzetti,et al.  Are higher degree even zonals really harmful for the LARES/LAGEOS frame-dragging experiment? , 2012 .

[116]  A. Kostelecký,et al.  Classical kinematics for Lorentz violation , 2010, 1008.5062.

[117]  I. H. Park,et al.  INDICATIONS OF INTERMEDIATE-SCALE ANISOTROPY OF COSMIC RAYS WITH ENERGY GREATER THAN 57 EeV IN THE NORTHERN SKY MEASURED WITH THE SURFACE DETECTOR OF THE TELESCOPE ARRAY EXPERIMENT , 2014, 1404.5890.

[118]  Jun Luo,et al.  Search for Lorentz violation in short-range gravity , 2014, 1412.8362.

[119]  Ignazio Ciufolini,et al.  Engineering and scientific aspects of LARES satellite , 2011 .

[120]  T. Damour,et al.  General relativistic celestial mechanics of binary systems. I. The post-newtonian motion , 1985 .

[121]  Ephraim Fischbach,et al.  The Search for Non-Newtonian Gravity , 1998 .

[122]  Asymptotic equivalence of the jackknife and infinitesimal jackknife variance estimators for some smooth statistics , 2003, math/0301363.

[123]  Chern-Simons modification of general relativity , 2003, gr-qc/0308071.

[124]  M. Soffel,et al.  Probing general relativity with radar astrometry in the inner solar system , 2011 .

[125]  Giampiero Sindoni,et al.  Testing General Relativity and gravitational physics using the LARES satellite , 2012, 1211.1374.

[126]  A. Kostelecký,et al.  $CPT$ violation and the standard model , 1997, hep-ph/9703464.

[127]  H. Belich,et al.  Lorentz violation and higher derivative gravity , 2014, 1409.5742.

[128]  Jay D. Tasson,et al.  The Standard-Model Extension and Gravitational Tests , 2016, Symmetry.

[129]  Talmadge,et al.  Model-independent constraints on possible modifications of Newtonian gravity. , 1988, Physical review letters.

[130]  Measuring the relativistic perigee advance with satellite laser ranging , 2001, gr-qc/0103088.

[131]  Slava G. Turyshev,et al.  Lunar Laser Ranging Contributions to Relativity and Geodesy , 2008 .

[132]  L. Iorio.  Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year , 2015, 1504.05789.

[133]  M. Kramer,et al.  Pulsars as probes of gravity and fundamental physics , 2016, 1606.03843.

[134]  J. R. Thomas,et al.  Search for correlations between HiRes stereo events and active galactic nuclei , 2008, 0804.0382.

[135]  Brane-antibrane inflation in orbifold and orientifold models , 2001, hep-th/0111025.

[136]  J. Tasson,et al.  What do we know about Lorentz invariance? , 2014, Reports on progress in physics. Physical Society.

[137]  J. Wahr,et al.  Tides for a convective Earth , 1999 .

[138]  G. Pucacco,et al.  Testing the gravitational interaction in the field of the Earth via satellite laser ranging and the Laser Ranged Satellites Experiment (LARASE) , 2015 .

[139]  George F. Smoot,et al.  General Relativity and Cosmology: Unsolved Questions and Future Directions , 2016, 1609.09781.

[140]  C. Le Poncin-Lafitte,et al.  Testing Lorentz Symmetry with Lunar Laser Ranging. , 2016, Physical review letters.

[141]  J. Tasson,et al.  Prospects for large relativity violations in matter-gravity couplings. , 2008, Physical review letters.

[142]  J. Lense,et al.  Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie , 1918 .

[143]  A. Kostelecký,et al.  Electrodynamics with Lorentz-violating operators of arbitrary dimension , 2009, 0905.0031.

[144]  S. Mouret.  Tests of fundamental physics with the Gaia mission through the dynamics of minor planets , 2011 .

[145]  N. Yunes,et al.  Strong binary pulsar constraints on Lorentz violation in gravity. , 2013, Physical review letters.

[146]  Giampiero Sindoni,et al.  Phenomenology of the Lense-Thirring effect in the Solar System: Measurement of frame-dragging with laser ranged satellites , 2012 .

[147]  W. D. Sitter.  On Einstein's Theory of Gravitation and its Astronomical Consequences , 1916 .

[148]  L. Iorio,et al.  OPTIS—An Einstein Mission for Improved Tests of Special and General Relativity , 2004 .

[149]  Marc-Thierry Jaekel,et al.  TESTING THE NEWTON LAW AT LONG DISTANCES , 2005 .

[150]  T. Jacobson,et al.  Gravity with a dynamical preferred frame , 2000, gr-qc/0007031.

[151]  Agnes Fienga,et al.  Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity , 2013, 1306.5569.

[152]  P. Freire,et al.  The relativistic pulsar-white dwarf binary PSR J1738+0333 - II. The most stringent test of scalar-tensor gravity , 2012, 1205.1450.

[153]  Sebastiano Ligori,et al.  Gravitation astrometric measurement experiment , 2012 .

[154]  S. Reynaud,et al.  Tests of general relativity in the solar system , 2007, 0801.3407.

[155]  A. Rivoldini,et al.  Testing Lorentz Symmetry with Planetary Orbital Dynamics , 2015, 1508.03478.

[156]  D. Champion,et al.  A new limit on local Lorentz invariance violation of gravity from solitary pulsars , 2013, 1307.2552.

[157]  H. Müller,et al.  Equivalence principle and bound kinetic energy. , 2013, Physical review letters.

[158]  A. Kostelecký,et al.  Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity , 2007, 0712.4119.

[159]  E. Standish.  The observational basis for JPL's DE 200, the planetary ephemerides of the Astronomical Almanac , 1990 .

[160]  R. Lynch,et al.  A millisecond pulsar in a stellar triple system , 2014, Nature.

[161]  M. Milgrom.  MOND effects in the inner Solar system , 2009, 0906.4817.

[162]  A. Fienga,et al.  The INPOP10a planetary ephemeris and its applications in fundamental physics , 2011 .

[163]  A. Kostelecký,et al.  Search for Lorentz violation in short-range gravity , 2014, 1412.8362.

[164]  V. Kreinovich,et al.  Relativistic reductions for radiointerferometric observables , 1983 .

[165]  A. Kostelecký.  Gravity, Lorentz violation, and the standard model , 2003, hep-th/0312310.

[166]  S. Lambert,et al.  Determination of the relativistic parameter gamma using very long baseline interferometry , 2009, 0903.1615.

[167]  E. Standish.  Testing alternate gravitational theories , 2009, Proceedings of the International Astronomical Union.

[168]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[169]  Q. Bailey.  Gravity Sector of the SME , 2016, 1607.07113.

[170]  Kenneth Nordtvedt,et al.  Testing relativity with laser ranging to the moon , 1968 .

[171]  I. Stairs.  Testing General Relativity with Pulsar Timing , 2003, Living reviews in relativity.

[172]  Chris Stormer,et al.  Explanatory Supplement to the Astronomical Almanac , 1995 .

[173]  F. Mignard,et al.  Gaia: Relativistic modelling and testing , 2009, Proceedings of the International Astronomical Union.

[174]  K. Thorne,et al.  Foundations for a Theory of Gravitation Theories , 1973 .

[175]  A. Kostelecký,et al.  Gravity from spontaneous Lorentz violation , 2009, 0901.0662.

[176]  Robert Lupton,et al.  Statistics in Theory and Practice , 2020 .

[177]  Steven Chu,et al.  Atom-interferometry tests of the isotropy of post-Newtonian gravity. , 2007, Physical review letters.

[178]  A. Peters,et al.  High-precision gravity measurements using atom interferometry , 1998 .

[179]  S. Reynaud,et al.  Post-Einsteinian tests of gravitation , 2005, gr-qc/0510068.

[180]  G. Renzetti,et al.  First results from LARES: An analysis , 2013 .

[181]  E. V. Pitjeva,et al.  EPM ephemerides and relativity , 2009, Proceedings of the International Astronomical Union.

[182]  A. Landragin,et al.  Underground operation at best sensitivity of the mobile LNE-SYRTE cold atom gravimeter , 2014 .

[183]  Pierre Touboul,et al.  The MICROSCOPE space mission , 2001 .

[184]  Clifford M. Will,et al.  Theory and Experiment in Gravitational Physics , 1982 .

[185]  Sabine Fenstermacher.  Handbook Of Pulsar Astronomy , 2016 .

[186]  Arnaldo J. Vargas,et al.  Lorentz and C P T tests with hydrogen, antihydrogen, and related systems , 2015, 1506.01706.

[187]  E. M. Standish,et al.  DE 102: a numerically integrated ephemeris of the moon and planets spanning forty-four centuries. , 1983 .

[188]  N. Wex.  The second post-Newtonian motion of compact binary-star systems with spin , 1995 .

[189]  R. Lehnert,et al.  Stability, causality, and Lorentz and CPT violation , 2000, hep-th/0012060.

[190]  S. Lambert,et al.  Lorentz symmetry and Very Long Baseline Interferometry , 2016, 1604.01663.

[191]  Samuel,et al.  Gravitational phenomenology in higher-dimensional theories and strings. , 1989, Physical review. D, Particles and fields.

[192]  David E. Smith,et al.  GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data , 2014, Geophysical research letters.

[193]  Jun Luo,et al.  Search for Lorentz invariance violation through tests of the gravitational inverse square law at short ranges , 2015, 1504.03280.

[194]  Small-Scale Anisotropy of Cosmic Rays above 1019 eV Observed with the Akeno Giant Air Shower Array , 1999, astro-ph/9902239.

[195]  J. Tasson,et al.  Constraints on Lorentz violation from gravitational Čerenkov radiation , 2015, 1508.07007.

[196]  C. Bordé.  Atomic interferometry with internal state labelling , 1989 .

[197]  Asymmetrically warped compactifications and gravitational Lorentz violation , 2003, hep-ph/0312245.

[198]  J. Tasson,et al.  Matter-gravity couplings and Lorentz violation , 2010, 1006.4106.

[199]  B. Foster.  Strong field effects on binary systems in Einstein-aether theory , 2007, 0706.0704.

[200]  A. Nelson,et al.  TESTS OF THE GRAVITATIONAL INVERSE-SQUARE LAW , 2003, hep-ph/0307284.

[201]  K. Nordtvedt.  Probing gravity to the second post-Newtonian order and to one part in 10 to the 7th using the spin axis of the sun , 1987 .

[202]  T. Damour,et al.  Tensor-multi-scalar theories of gravitation , 1991 .

[203]  LASER ASTROMETRIC TEST OF RELATIVITY: SCIENCE, TECHNOLOGY AND MISSION DESIGN , 2007, gr-qc/0701102.

[204]  Badr N. Alsuwaidan,et al.  Gravity Probe B: final results of a space experiment to test general relativity. , 2011, Physical review letters.

[205]  R. Ruffini,et al.  Nonlinear Gravitodynamics: The Lense-Thirring Effect , 2003 .

[206]  Lower bound on the propagation speed of gravity from gravitational Cherenkov radiation , 2001, hep-ph/0106220.

[207]  A. Kostelecký.  RiemannFinsler geometry and Lorentz-violating kinematics , 2011, 1104.5488.

[208]  A new test of conservation laws and Lorentz invariance in relativistic gravity , 1996, gr-qc/9606062.

[209]  S. Carroll,et al.  Noncommutative field theory and Lorentz violation. , 2001, Physical review letters.

[210]  S. Capozziello,et al.  GRAVITATIONAL CHERENKOV RADIATION FROM EXTENDED THEORIES OF GRAVITY , 2012, 1206.6681.

[211]  D. Lucchesi,et al.  LAGEOS II pericenter general relativistic precession (1993-2005): Error budget and constraints in gravitational physics , 2014 .

[212]  C. Stubbs,et al.  Testing for Lorentz violation: constraints on standard-model-extension parameters via lunar laser ranging. , 2007, Physical review letters.

[213]  M. Seifert.  Vector models of gravitational Lorentz symmetry breaking , 2009, 0903.2279.

[214]  Lorenzo Iorio.  Will the recently approved LARES mission be able to measure the Lense–Thirring effect at 1%? , 2008 .

[215]  A. Kostelecký,et al.  Data Tables for Lorentz and CPT Violation , 2008, 0801.0287.

[216]  Giampiero Sindoni,et al.  Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models , 2009 .

[217]  C. Will,et al.  Conservation Laws and Preferred Frames in Relativistic Gravity. II. Experimental Evidence to Rule Out Preferred-Frame Theories of Gravity , 1972 .

[218]  S. Merkowitz.  Tests of Gravity Using Lunar Laser Ranging , 2010, Living reviews in relativity.

[219]  A. Kostelecký,et al.  Testing local Lorentz invariance with gravitational waves , 2016, 1602.04782.

[220]  Luciano Iess,et al.  Cassini Radio Science , 2004 .

[221]  Rodolfo Gambini,et al.  Nonstandard optics from quantum space-time , 1999 .

[222]  Lijing Shao.  New pulsar limit on local Lorentz invariance violation of gravity in the standard-model extension , 2014, 1412.2320.

[223]  K. Thorne,et al.  Theoretical Frameworks for Testing Relativistic Gravity. I. Foundations , 1971 .

[224]  H. Lichtenegger,et al.  Phenomenology of the Lense-Thirring effect in the solar system , 2010, 1009.3225.

[225]  E. Pitjeva,et al.  Constraints on dark matter in the solar system , 2013, 1306.5534.

[226]  J. Novak,et al.  External field effect of modified Newtonian dynamics in the Solar system , 2010, 1010.1349.

[227]  W. Folkner,et al.  Constraints on modified Newtonian dynamics theories from radio tracking data of the Cassini spacecraft , 2014, 1402.6950.