Skip to main content

Use of Geodesy and Geophysics Measurements to Probe the Gravitational Interaction

  • Chapter
  • First Online:
Relativistic Geodesy

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 196))

Abstract

Despite its extraordinary successes, the theory of General Relativity is likely not the ultimate theory of the gravitational interaction. Indeed, General Relativity as such is a classical theory and is therefore incomplete since it does not include any quantum effects. Moreover, most physicists agree that GR and the Standard Model are only effective field theories that are low-energy approximation of a more fundamental and more general theory that would provide a unified description of all the fundamental interactions. On the observational side, Dark Matter and Dark Energy are required to explain most of astrophysical and cosmological observations and very few is known and this two Dark components, which is sometimes interpreted as an hint that our theory of gravitation is incomplete. For these reasons, General Relativity is confronted to an increasing number of measurements, searching for deviations in more and more frameworks that extend General Relativity. Amongst all the measurements used to search for and to constrain deviations from General Relativity, a observations developed in the context of geodesy and geophysics are playing an important role like for example atomic clocks comparison, gravimetry measurements, satellite and lunar laser ranging, very long baseline interferometry, etc ...In this communication, we present briefly each of these geodesic/geophysics measurements and show how they have recently been used to constrain extensions of General Relativity, model of Dark Matter or of Dark Energy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. B. Famaey, S.S. McGaugh, Modified Newtonian dynamics (MOND): observational phenomenology and relativistic. Living Rev Relativ 15, 10 (2012)

    Article  ADS  Google Scholar 

  2. T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rep. 513, 1–189 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  3. C.M. Will, The confrontation between general relativity and experiment. Living Rev. Relativ. 17, 4 (2014)

    Article  ADS  MATH  Google Scholar 

  4. G. Lion, I. Panet, P. Wolf, C. Guerlin, S. Bize, P. Delva, Determination of a high spatial resolution geopotential model using atomic clock comparisons. J. Geodesy 91, 597–611 (2017)

    Article  ADS  Google Scholar 

  5. Microg Lacoste. FG5-X and FGL absolute gravity meters

    Google Scholar 

  6. \(\mu \) QUANS. Absolute quantum gravimeter

    Google Scholar 

  7. C.W. Chou, D.B. Hume, J.C.J. Koelemeij, D.J. Wineland, T. Rosenband, Frequency comparison of two high-accuracy Al\(^{+}\) optical clocks. Phys. Rev. Lett. 104(7), 070802 (2010)

    Article  ADS  Google Scholar 

  8. K. Beloy, N. Hinkley, N.B. Phillips, J.A. Sherman, M. Schioppo, J. Lehman, A. Feldman, L.M. Hanssen, C.W. Oates, A.D. Ludlow, Atomic clock with \(1 {\times }10^{-18}\) room-temperature blackbody stark uncertainty. Phys. Rev. Lett. 113(26), 260801 (2014)

    Article  ADS  Google Scholar 

  9. T.L. Nicholson, S.L. Campbell, R.B. Hutson, G.E. Marti, B.J. Bloom, R.L. McNally, W. Zhang, M.D. Barrett, M.S. Safronova, G.F. Strouse, W.L. Tew, J. Ye, Systematic evaluation of an atomic clock at \(2 {\times } 10^{-18}\) total uncertainty. Nat. Commun. 6, 6896 (2015)

    Article  ADS  Google Scholar 

  10. I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, H. Katori, Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015)

    Article  ADS  Google Scholar 

  11. N. Huntemann, C. Sanner, B. Lipphardt, C. Tamm, E. Peik, Single-ion atomic clock with \(3 {\times }10^{-18}\) systematic uncertainty. Phys. Rev. Lett. 116(6), 063001 (2016)

    Article  ADS  Google Scholar 

  12. Peter Wolf. Viewpoint: Next generation clock networks. Physical Review: Viewpoint, Physics 9, 51, May 11, 2016 2016

    Google Scholar 

  13. H. Denker, L. Timmen, C. Voigt, S. Weyers, E. Peik, H.S. Margolis, P. Delva, P. Wolf, G. Petit, Geodetic methods to determine the relativistic redshift at the level of 10 (-18) - 18 in the context of international timescales: a review and practical results. J. Geodesy 92, 487–516 (2018)

    Article  ADS  Google Scholar 

  14. T.E. Mehlstäubler, G. Grosche, C. Lisdat, P.O. Schmidt, H. Denker, Atomic clocks for geodesy. Rep. Prog. Phys. 81(6), 064401 (2018)

    Article  ADS  Google Scholar 

  15. I. Ciufolini, E. Pavlis, F. Chieppa, E. Fernandes-Vieira, J. Perez-Mercader, Test of general relativity and measurement of the lense-thirring effect with two earth satellites. Science 279, 2100 (1998)

    Article  ADS  Google Scholar 

  16. I. Ciufolini, E.C. Pavlis, A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature 431, 958–960 (2004)

    Article  ADS  Google Scholar 

  17. I. Ciufolini, A. Paolozzi, E.C. Pavlis, R. Koenig, J. Ries, V. Gurzadyan, R. Matzner, R. Penrose, G. Sindoni, C. Paris, H. Khachatryan, S. Mirzoyan, A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model. Measurement of Earth’s dragging of inertial frames. Eur. Phys. J. C 76, 120 (2016)

    Google Scholar 

  18. J.O. Dickey, P.L. Bender, J.E. Faller, X.X. Newhall, R.L. Ricklefs, J.G. Ries, P.J. Shelus, C. Veillet, A.L. Whipple, J.R. Wiant, J.G. Williams, C.F. Yoder, Lunar laser ranging: a continuing legacy of the apollo program. Science 265, 482–490 (1994)

    Article  ADS  Google Scholar 

  19. N.P. Pitjev, E.V. Pitjeva, Constraints on dark matter in the solar system. Astron. Lett. 39, 141–149 (2013)

    Article  ADS  Google Scholar 

  20. E.M. Standish, The JPL planetary ephemerides. Celest. Mech. 26, 181–186 (1982)

    Article  ADS  Google Scholar 

  21. X.X. Newhall, E.M. Standish, J.G. Williams, DE 102 - A numerically integrated ephemeris of the moon and planets spanning forty-four centuries. A&A 125, 150–167 (1983)

    ADS  MATH  Google Scholar 

  22. E.M. Standish Jr., The observational basis for JPL’s DE 200, the planetary ephemerides of the Astronomical Almanac. A&A 233, 252–271 (1990)

    ADS  Google Scholar 

  23. E.M. Standish, Testing alternate gravitational theories, in IAU Symposium, ed. by S.A. Klioner, P.K. Seidelmann, M.H. Soffel, vol. 261 (2010), pp. 179–182

    Article  Google Scholar 

  24. E.M. Standish, J.G. Williams, Orbital ephemerides of the Sun, Moon, and Planets, in Explanatory Supplement to the Astronomical Almanac, ed. by S.E. Urban, P.K. Seidelmann, 3rd edn. (Univeristy Science Books, 2012), pp. 305–346

    Google Scholar 

  25. W.M. Folkner, J.G. Williams, D.H. Boggs, R. Park, P. Kuchynka, The planetary and lunar ephemeris DE 430 and DE431. IPN Prog. Rep. 42(196) (2014)

    Google Scholar 

  26. A. Hees, W.M. Folkner, R.A. Jacobson, R.S. Park, Constraints on modified Newtonian dynamics theories from radio tracking data of the Cassini spacecraft. Phys. Rev. D 89(10), 102002 (2014)

    Article  ADS  Google Scholar 

  27. A. Fienga, H. Manche, J. Laskar, M. Gastineau, INPOP06: a new numerical planetary ephemeris. A&A 477, 315–327 (2008)

    Article  ADS  Google Scholar 

  28. A. Fienga, J. Laskar, T. Morley, H. Manche, P. Kuchynka, C. Le Poncin-Lafitte, F. Budnik, M. Gastineau, L. Somenzi, INPOP08, a 4-D planetary ephemeris: from asteroid and time-scale computations to ESA Mars Express and Venus Express contributions. A&A 507, 1675–1686 (2009)

    Article  ADS  Google Scholar 

  29. A. Fienga, J. Laskar, P. Kuchynka, C. Le Poncin-Lafitte, H. Manche, M. Gastineau, Gravity tests with INPOP planetary ephemerides, in IAU Symposium, ed. by S.A. Klioner, P.K. Seidelmann, M.H. Soffel, vol. 261 (2010), pp. 159–169

    Article  Google Scholar 

  30. A. Fienga, J. Laskar, P. Kuchynka, H. Manche, G. Desvignes, M. Gastineau, I. Cognard, G. Theureau, The INPOP10a planetary ephemeris and its applications in fundamental physics. Celest. Mech. Dyn. Astrono. 111(3), 363–385 (2011)

    Article  ADS  Google Scholar 

  31. A.K. Verma, A. Fienga, J. Laskar, H. Manche, M. Gastineau, Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity. A&A 561, A115 (2014)

    Article  ADS  Google Scholar 

  32. A. Fienga, J. Laskar, P. Exertier, H. Manche, M. Gastineau, Numerical estimation of the sensitivity of INPOP planetary ephemerides to general relativity parameters. Celest. Mech. Dyn. Astron. 123, 325–349 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  33. E.V. Pitjeva, High-precision ephemerides of planets EPM and determination of some astronomical constants. Solar Syst. Res. 39, 176–186 (2005)

    Article  ADS  Google Scholar 

  34. E.V. Pitjeva, EPM ephemerides and relativity, in Proceedings of IAU Symposium 261, ed. by S.A. Klioner, P.K. Seidelmann, M.H. Soffel (2010), pp. 170–178

    Article  Google Scholar 

  35. E.V. Pitjeva, N.P. Pitjev, Relativistic effects and dark matter in the Solar system from observations of planets and spacecraft. MNRAS 432, 3431–3437 (2013)

    Article  ADS  Google Scholar 

  36. E.V. Pitjeva, Updated IAA RAS planetary ephemerides-EPM2011 and their use in scientific research. Solar Syst. Res. 47, 386–402 (2013)

    Article  ADS  Google Scholar 

  37. E.V. Pitjeva, N.P. Pitjev, Development of planetary ephemerides EPM and their applications. Celest. Mech. Dyn. Astron. 119, 237–256 (2014)

    Article  ADS  Google Scholar 

  38. A.L. Fey, D. Gordon, C.S. Jacobs, C. Ma, R.A. Gaume, E.F. Arias, G. Bianco, D.A. Boboltz, S. Böckmann, S. Bolotin, P. Charlot, A. Collioud, G. Engelhardt, J. Gipson, A.-M. Gontier, R. Heinkelmann, S. Kurdubov, S. Lambert, S. Lytvyn, D.S. MacMillan, Z. Malkin, A. Nothnagel, R. Ojha, E. Skurikhina, J. Sokolova, J. Souchay, O.J. Sovers, V. Tesmer, O. Titov, G. Wang, V. Zharov, The second realization of the international celestial reference frame by very long baseline interferometry. AJ 150, 58 (2015)

    Article  ADS  Google Scholar 

  39. M. Soffel, S.A. Klioner, G. Petit, P. Wolf, S.M. Kopeikin, P. Bretagnon, V.A. Brumberg, N. Capitaine, T. Damour, T. Fukushima, B. Guinot, T.-Y. Huang, L. Lindegren, C. Ma, K. Nordtvedt, J.C. Ries, P.K. Seidelmann, D. Vokrouhlický, C.M. Will, C. Xu, The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement. Astron. J. 126, 2687–2706 (2003)

    Article  ADS  Google Scholar 

  40. A. Einstein, Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes. Annalen der Physik 340, 898–908 (1911). Traduction anglaise dans [256]

    Article  ADS  MATH  Google Scholar 

  41. K.S. Thorne, C.M. Will, Theoretical frameworks for testing relativistic gravity I. Foundations. ApJ 163, 595 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  42. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation. Physics Series (W. H. Freeman, 1973)

    Google Scholar 

  43. C.M. Will, Theory and Experiment in Gravitational Physics (1993)

    Google Scholar 

  44. A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik 354, 769–822 (1916). Traduction anglaise dans [256]

    Article  ADS  MATH  Google Scholar 

  45. D. Lovelock, The Einstein tensor and its generalizations. J. Math. Phys. 12, 498–501 (1971)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. D. Lovelock, The Four-Dimensionality of Space and the Einstein Tensor. J. Math. Phys. 13, 874–876 (1972)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, S.H. Aronson, Reanalysis of the Eotvos experiment. Phys. Rev. Lett. 56, 3–6 (1986)

    Article  ADS  Google Scholar 

  48. C. Talmadge, J.-P. Berthias, R.W. Hellings, E.M. Standish, Model-independent constraints on possible modifications of Newtonian gravity. Phys. Rev. Lett. 61, 1159–1162 (1988)

    Article  ADS  Google Scholar 

  49. E. Fischbach, C. Talmadge, Six years of the fifth force. Nature 356, 207–215 (1992)

    Article  ADS  Google Scholar 

  50. E. Fischbach, C.L. Talmadge, The Search for Non-Newtonian Gravity, Aip-Press Series (Springer, Berlin, 1999)

    Book  MATH  Google Scholar 

  51. E.G. Adelberger, J.H. Gundlach, B.R. Heckel, S. Hoedl, S. Schlamminger, Torsion balance experiments: a low-energy frontier of particle physics. Prog. Part. Nucl. Phys. 62, 102–134 (2009)

    Article  ADS  Google Scholar 

  52. A. Hees, B. Lamine, S. Reynaud, M.-T. Jaekel, C. Le Poncin-Lafitte, V. Lainey, A. Füzfa, J.-M. Courty, V. Dehant, P. Wolf, Radioscience simulations in general relativity and in alternative theories of gravity. Class. Quantum Gravity 29(23), 235027 (2012)

    Article  ADS  MATH  Google Scholar 

  53. A. Hees, W. Folkner, R. Jacobson, R. Park, B. Lamine, C. Le Poncin-Lafitte, P. Wolf, Tests of gravitation at Solar System scales beyond the PPN formalism, in Journées 2013 Systèmes de référence spatio-temporels ed. by N. Capitaine (2014), pp. 241–244

    Google Scholar 

  54. Q.G. Bailey, V.A. Kostelecký, Signals for Lorentz violation in post-Newtonian gravity. Phys. Rev. D 74(4), 045001 (2006)

    Article  ADS  Google Scholar 

  55. V.A. Kostelecký, J.D. Tasson, Matter-gravity couplings and Lorentz violation. Phys. Rev. D 83(1), 016013 (2011)

    Article  ADS  Google Scholar 

  56. A. Hees, Q. Bailey, A. Bourgoin, H. Pihan-Le Bars, C. Guerlin, C. Le Poncin-Lafitte, Tests of Lorentz symmetry in the gravitational sector. Universe 2, 30 (2016)

    Article  ADS  Google Scholar 

  57. J.D. Tasson, The standard-model extension and gravitational tests. Symmetry 8, 111 (2016)

    Article  MathSciNet  Google Scholar 

  58. M. Milgrom, MOND effects in the inner Solar system. MNRAS 399, 474–486 (2009)

    Article  ADS  Google Scholar 

  59. L. Blanchet, J. Novak, External field effect of modified Newtonian dynamics in the Solar system. MNRAS 412, 2530–2542 (2011)

    Article  ADS  Google Scholar 

  60. M.-T. Jaekel, S. Reynaud, Post-Einsteinian tests of linearized gravitation. Class. Quantum Gravity 22, 2135–2157 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  61. M.-T. Jaekel, S. Reynaud, Post-Einsteinian tests of gravitation. Class. Quantum Gravity 23, 777–798 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. A. Avilez-Lopez, A. Padilla, P.M. Saffin, C. Skordis, The parametrized post-Newtonian-vainshteinian formalism. J. Cosmol. Astropart. Phys. 6, 044 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  63. M. Hohmann, Parametrized post-Newtonian limit of Horndeski’s gravity theory. Phys. Rev. D 92(6), 064019 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  64. G.L. Smith, C.D. Hoyle, J.H. Gundlach, E.G. Adelberger, B.R. Heckel, H.E. Swanson, Short-range tests of the equivalence principle. Phys. Rev. D 61(2), 022001 (1999)

    Article  ADS  Google Scholar 

  65. S. Schlamminger, K.-Y. Choi, T.A. Wagner, J.H. Gundlach, E.G. Adelberger, Test of the equivalence principle using a rotating torsion balance. Phys. Rev. Lett. 100(4), 041101 (2008)

    Article  ADS  Google Scholar 

  66. T.A. Wagner, S. Schlamminger, J.H. Gundlach, E.G. Adelberger, Torsion-balance tests of the weak equivalence principle. Class. Quantum Gravity 29(18), 184002 (2012)

    Article  ADS  Google Scholar 

  67. V. Viswanathan, A. Fienga, O. Minazzoli, L. Bernus, J. Laskar, M. Gastineau, The new lunar ephemeris INPOP17a and its application to fundamental physics. MNRAS 476, 1877–1888 (2018)

    Article  ADS  Google Scholar 

  68. K. Nordtvedt, Testing relativity with laser ranging to the Moon. Phys. Rev. 170, 1186–1187 (1968)

    Article  ADS  Google Scholar 

  69. J.G. Williams, S.G. Turyshev, D.H. Boggs, Lunar laser ranging tests of the equivalence principle with the Earth and Moon. Inte. J. Mod. Phys. D 18, 1129–1175 (2009)

    Article  ADS  MATH  Google Scholar 

  70. J.G. Williams, S.G. Turyshev, D. Boggs, Lunar laser ranging tests of the equivalence principle. Class. Quantum Gravity 29(18), 184004 (2012)

    Article  ADS  Google Scholar 

  71. C. Courde, J.M. Torre, E. Samain, G. Martinot-Lagarde, M. Aimar, D. Albanese, P. Exertier, A. Fienga, H. Mariey, G. Metris, H. Viot, V. Viswanathan, Lunar laser ranging in infrared at the Grasse laser station. A&A 602, A90 (2017)

    Article  ADS  Google Scholar 

  72. P. Touboul, G. Métris, M. Rodrigues, Y. André, Q. Baghi, J. Bergé, D. Boulanger, S. Bremer, P. Carle, R. Chhun, B. Christophe, V. Cipolla, T. Damour, P. Danto, H. Dittus, P. Fayet, B. Foulon, C. Gageant, P.-Y. Guidotti, D. Hagedorn, E. Hardy, P.-A. Huynh, H. Inchauspe, P. Kayser, S. Lala, C. Lämmerzahl, V. Lebat, P. Leseur, F. Liorzou, M. List, F. Löffler, I. Panet, B. Pouilloux, P. Prieur, A. Rebray, S. Reynaud, B. Rievers, A. Robert, H. Selig, L. Serron, T. Sumner, N. Tanguy, P. Visser, MICROSCOPE mission: first results of a space test of the equivalence principle. Phys. Rev. Lett. 119(23), 231101 (2017)

    Article  ADS  Google Scholar 

  73. J. Bergé, P. Brax, G. Métris, M. Pernot-Borràs, P. Touboul, J.-P. Uzan, MICROSCOPE mission: first constraints on the violation of the weak equivalence principle by a light scalar dilaton. Phys. Rev. Lett. 120(14), 141101 (2018)

    Article  ADS  Google Scholar 

  74. P. Fayet. MICROSCOPE limits for new long-range forces and implications for unified theories. ArXiv e-prints (2017)

    Google Scholar 

  75. A. Peters, K.Y. Chung, S. Chu, Measurement of gravitational acceleration by dropping atoms. Nature 400, 849–852 (1999)

    Article  ADS  Google Scholar 

  76. A. Peters, K.Y. Chung, S. Chu, High-precision gravity measurements using atom interferometry. Metrologia 38, 25–61 (2001)

    Article  ADS  Google Scholar 

  77. S. Merlet, Q. Bodart, N. Malossi, A. Landragin, F. Pereira Dos Santos, O. Gitlein, L. Timmen, SHORT COMMUNICATION: comparison between two mobile absolute gravimeters: optical versus atomic interferometers. Metrologia 47, L9–L11 (2010)

    Article  ADS  Google Scholar 

  78. L. Zhou, S. Long, B. Tang, X. Chen, F. Gao, W. Peng, W. Duan, J. Zhong, Z. Xiong, J. Wang, Y. Zhang, M. Zhan, Test of equivalence principle at 1 0\(^{-8}\) level by a dual-species double-diffraction Raman atom interferometer. Phys. Rev. Lett. 115(1), 013004 (2015)

    Article  ADS  Google Scholar 

  79. F.W. Hehl, P. von der Heyde, G.D. Kerlick, J.M. Nester, General relativity with spin and torsion: foundations and prospects. Rev. Mod. Phys. 48, 393–416 (1976)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  80. A. Peres, Test of equivalence principle for particles with spin. Phys. Rev. D 18, 2739–2740 (1978)

    Article  ADS  Google Scholar 

  81. B. Mashhoon, Gravitational couplings of intrinsic spin. Class. Quantum Gravity 17, 2399–2409 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  82. Y.N. Obukhov, Spin, gravity, and inertia. Phys. Rev. Lett. 86, 192–195 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  83. W.-T. Ni, Searches for the role of spin and polarization in gravity. Rep. Prog. Phys. 73(5), 056901 (2010)

    Article  ADS  Google Scholar 

  84. W.-T. Ni, Searches for the role of spin and polarization in gravity: a five-year update, in International Journal of Modern Physics Conference Series, vol. 40 (2016), pp. 1660010–146

    Google Scholar 

  85. M.G. Tarallo, T. Mazzoni, N. Poli, D.V. Sutyrin, X. Zhang, G.M. Tino, Test of einstein equivalence principle for 0-spin and half-integer-spin atoms: search for spin-gravity coupling effects. Phys. Rev. Lett. 113(2), 023005 (2014)

    Article  ADS  Google Scholar 

  86. S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, G. Bonomi, P. Bräunig, J. Bremer, R. S. Brusa, L. Cabaret, C. Canali, R. Caravita, F. Castelli, G. Cerchiari, S. Cialdi, D. Comparat, G. Consolati, J. H. Derking, S. Di Domizio, L. Di Noto, M. Doser, A. Dudarev, A. Ereditato, R. Ferragut, A. Fontana, P. Genova, M. Giammarchi, A. Gligorova, S. N. Gninenko, S. Haider, J. Harasimovicz, S. D. Hogan, T. Huse, E. Jordan, L. V. Jørgensen, T. Kaltenbacher, J. Kawada, A. Kellerbauer, M. Kimura, A. Knecht, D. Krasnický, V. Lagomarsino, A. Magnani, S. Mariazzi, V. A. Matveev, F. Moia, G. Nebbia, P. Nédélec, M. K. Oberthaler, N. Pacifico, V. Petráček, C. Pistillo, F. Prelz, M. Prevedelli, C. Regenfus, C. Riccardi, O. Røhne, A. Rotondi, H. Sandaker, P. Scampoli, A. Sosa, J. Storey, M. A. Subieta Vasquez, M. Špaček, G. Testera, D. Trezzi, R. Vaccarone, C. P. Welsch, and S. Zavatarelli. Prospects for measuring the gravitational free-fall of antihydrogen with emulsion detectors. J. Instrum. 8, 8013P (2013)

    Google Scholar 

  87. P. Perez, Y. Sacquin, The GBAR experiment: gravitational behaviour of antihydrogen at rest. Class. Quantum Gravity 29(18), 184008 (2012)

    Article  ADS  Google Scholar 

  88. L. Hui, A. Nicolis, Proposal for an observational test of the vainshtein mechanism. Phys. Rev. Lett. 109(5), 051304 (2012)

    Article  ADS  Google Scholar 

  89. J. Sakstein, B. Jain, J.S. Heyl, L. Hui, Tests of gravity theories using supermassive black holes. ApJl 844, L14 (2017)

    Article  ADS  Google Scholar 

  90. J.A. Frieman, B.-A. Gradwohl, Dark matter and the equivalence principle. Phys. Rev. Lett. 67, 2926–2929 (1991)

    Article  ADS  Google Scholar 

  91. B.-A. Gradwohl, J.A. Frieman, Dark matter, long-range forces, and large-scale structure. ApJ 398, 407–424 (1992)

    Article  ADS  Google Scholar 

  92. S.M. Carroll, S. Mantry, M.J. Ramsey-Musolf, C.W. Stubbs, Dark-matter-induced violation of the weak equivalence principle. Phys. Rev. Lett. 103(1), 011301 (2009)

    Article  ADS  Google Scholar 

  93. S.M. Carroll, S. Mantry, M.J. Ramsey-Musolf, Implications of a scalar dark force for terrestrial experiments. Phys. Rev. D 81(6), 063507 (2010)

    Article  ADS  Google Scholar 

  94. M. Kesden, M. Kamionkowski, Tidal tails test the equivalence principle in the dark-matter sector. Phys. Rev. D 74(8), 083007 (2006)

    Article  ADS  Google Scholar 

  95. M. Kesden, M. Kamionkowski, Galilean equivalence for galactic dark matter. Phys. Rev. Lett. 97(13), 131303 (2006)

    Article  ADS  Google Scholar 

  96. C.W. Stubbs, Experimental limits on any long range nongravitational interaction between dark matter and ordinary matter. Phys. Rev. Lett. 70, 119–122 (1993)

    Article  ADS  Google Scholar 

  97. Y. Bai, J. Salvado, B.A. Stefanek, Cosmological constraints on the gravitational interactions of matter and dark matter. J. Cosmol. Astropart. Phys. 10, 029 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  98. A. Hees, T. Do, A.M. Ghez, G.D. Martinez, S. Naoz, E.E. Becklin, A. Boehle, S. Chappell, D. Chu, A. Dehghanfar, K. Kosmo, J.R. Lu, K. Matthews, M.R. Morris, S. Sakai, R. Schödel, G. Witzel, Testing general relativity with stellar orbits around the supermassive black hole in our galactic center. Phys. Rev. Lett. 118(21), 211101 (2017)

    Article  ADS  Google Scholar 

  99. T. Damour, G.W. Gibbons, C. Gundlach, Dark matter, time-varying G, and a dilaton field. Phys. Rev. Lett. 64, 123–126 (1990)

    Article  ADS  Google Scholar 

  100. J.-M. Alimi, A. Füzfa, Is dark energy abnormally weighting? Int. J. Mod. Phys. D 16, 2587–2592 (2007)

    Article  ADS  Google Scholar 

  101. J.-M. Alimi, A. Füzfa, The abnormally weighting energy hypothesis: the missing link between dark matter and dark energy. J. Cosmology Astropart. Phys. 9, 14 (2008)

    Article  ADS  Google Scholar 

  102. A. Füzfa, J.-M. Alimi, Toward a unified description of dark energy and dark matter from the abnormally weighting energy hypothesis. Phys. Rev. D 75(12), 123007 (2007)

    Article  ADS  Google Scholar 

  103. N. Mohapi, A. Hees, J. Larena, Test of the equivalence principle in the dark sector on galactic scales. J. Cosmol. Astropart. Phys. 3, 032 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  104. D. Mattingly, Modern tests of lorentz invariance. Living Rev. Relativ. 8, 5 (2005)

    Google Scholar 

  105. V.W. Hughes, H.G. Robinson, V. Beltran-Lopez, Upper limit for the anisotropy of inertial mass from nuclear resonance experiments. Phys. Rev. Lett. 4, 342–344 (1960)

    Article  ADS  Google Scholar 

  106. R.W.P. Drever, A search for anisotropy of inertial mass using a free precession technique. Philos. Mag. 6, 683–687 (1961)

    Article  ADS  Google Scholar 

  107. T.E. Chupp, R.J. Hoare, R.A. Loveman, E.R. Oteiza, J.M. Richardson, M.E. Wagshul, A.K. Thompson, Results of a new test of local Lorentz invariance: a search for mass anisotropy in \(^{21}\)Ne. Phys. Rev. Lett. 63, 1541–1545 (1989)

    Article  ADS  Google Scholar 

  108. S.K. Lamoreaux, J.P. Jacobs, B.R. Heckel, F.J. Raab, E.N. Fortson, New limits on spatial anisotropy from optically-pumped sup201Hg and \(^{199}\)Hg. Phys. Rev. Lett. 57, 3125–3128 (1986)

    Article  ADS  Google Scholar 

  109. J.D. Prestage, J.J. Bollinger, W.M. Itano, D.J. Wineland, Limits for spatial anisotropy by use of nuclear-spin-polarized Be-9(+) ions. Phys. Rev. Lett. 54, 2387–2390 (1985)

    Article  ADS  Google Scholar 

  110. M.P. Haugan, C.M. Will, Modern tests of special relativity. Phys. Today 40, 69–86 (1987)

    Article  ADS  Google Scholar 

  111. A. Brillet, J.L. Hall, Improved laser test of the isotropy of space. Phys. Rev. Lett. 42, 549–552 (1979)

    Article  ADS  Google Scholar 

  112. P.L. Stanwix, M.E. Tobar, P. Wolf, C.R. Locke, E.N. Ivanov, Improved test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire oscillators. Phys. Rev. D 74(8), 081101 (2006)

    Article  ADS  Google Scholar 

  113. P. Wolf, S. Bize, A. Clairon, A.N. Luiten, G. Santarelli, M.E. Tobar, Tests of Lorentz invariance using a microwave resonator. Phys. Rev. Lett. 90(6), 060402 (2003)

    Article  ADS  MATH  Google Scholar 

  114. H.P. Robertson, Postulate versus observation in the special theory of relativity. Rev. Mod. Phys. 21, 378–382 (1949)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  115. R. Mansouri, R.U. Sexl, A test theory of special relativity. I - simultaneity and clock synchronization. II - first order tests. Gen. Relativ. Gravitat. 8, 497–513 (1977)

    Google Scholar 

  116. R. Mansouri, R.U. Sexl. A test theory of special relativity: II. first order tests. Gen. Relativ. Gravit. 8, 515–524 (1977)

    Article  ADS  Google Scholar 

  117. R. Mansouri, R.U. Sexl, A test theory of special relativity: III Second-order tests. Gen. Relativ. Gravit. 8, 809–814 (1977)

    Article  ADS  Google Scholar 

  118. S. Reinhardt, G. Saathoff, H. Buhr, L.A. Carlson, A. Wolf, D. Schwalm, S. Karpuk, C. Novotny, G. Huber, M. Zimmermann, R. Holzwarth, T. Udem, T.W. Hänsch, G. Gwinner, Test of relativistic time dilation with fast optical atomic clocks at different velocities. Nat. Phys. 3, 861–864 (2007)

    Article  Google Scholar 

  119. B. Botermann, D. Bing, C. Geppert, G. Gwinner, T.W. Hänsch, G. Huber, S. Karpuk, A. Krieger, T. Kühl, W. Nörtershäuser, C. Novotny, S. Reinhardt, R. Sánchez, D. Schwalm, T. Stöhlker, A. Wolf, G. Saathoff, Test of time dilation using stored Li\(^{+}\) ions as clocks at relativistic speed. Phys. Rev. Lett. 113(12), 120405 (2014)

    Article  ADS  Google Scholar 

  120. C.M. Will, Clock synchronization and isotropy of the one-way speed of light. Phys. Rev. D 45, 403–411 (1992)

    Article  ADS  Google Scholar 

  121. P. Wolf, G. Petit, Satellite test of special relativity using the global positioning system. Phys. Rev. A 56, 4405–4409 (1997)

    Article  ADS  Google Scholar 

  122. J. Lodewyck, S. Bilicki, E. Bookjans, J.-L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guéna, M. Abgrall, P. Rosenbusch, S. Bize, Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock. Metrologia 53, 1123 (2016)

    Article  ADS  Google Scholar 

  123. R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D.G. Rovera, B. Nagórny, R. Gartman, P.G. Westergaard, M.E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, J. Lodewyck, Experimental realization of an optical second with strontium lattice clocks. Nat. Commun. 4, 2109 (2013)

    Article  Google Scholar 

  124. S. Falke, N. Lemke, C. Grebing, B. Lipphardt, S. Weyers, V. Gerginov, N. Huntemann, C. Hagemann, A. Al-Masoudi, S. Häfner, S. Vogt, U. Sterr, C. Lisdat, A strontium lattice clock with \(3 {\times } 10^{-17}\) inaccuracy and its frequency. New J. Phys. 16(7), 073023 (2014)

    Article  ADS  Google Scholar 

  125. C. Grebing, A. Al-Masoudi, D. Sören, H. Sebastian, G. Vladislav, W. Stefan, L. Burghard, R. Fritz, S. Uwe, L. Christian, Realization of a timescale with an accurate optical lattice clock. Optica 3(6), 563–569 (2016)

    Article  Google Scholar 

  126. I.R. Hill, R. Hobson, W. Bowden, E.M. Bridge, S. Donnellan, E.A. Curtis, P. Gill, A low maintenance Sr optical lattice clock. In Journal of Physics Conference Series, volume 723 of Journal of Physics Conference Series, page 012019, June 2016

    Google Scholar 

  127. C. Lisdat, G. Grosche, N. Quintin, C. Shi, S.M.F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, P.-E. Pottie, A clock network for geodesy and fundamental science. Nat. Commun. 7, 12443 (2016)

    Article  ADS  Google Scholar 

  128. P.A. Williams, W.C. Swann, N.R. Newbury, High-stability transfer of an optical frequency over long fiber-optic links. J. Opt. Soc. Am. B Opt. Phys. 25, 1284 (2008)

    Article  ADS  Google Scholar 

  129. G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, H. Schnatz, Optical frequency transfer via 146 km fiber link with \(10\hat{}\)-19 relative accuracy. Opt. Lett. 34, 2270 (2009)

    Article  ADS  Google Scholar 

  130. G. Grosche, Eavesdropping time and frequency: phase noise cancellation along a time-varying path, such as an optical fiber. Opt. Lett. 39, 2545 (2014)

    Article  ADS  Google Scholar 

  131. F. Stefani, O. Lopez, A. Bercy, W.-K. Lee, C. Chardonnet, G. Santarelli, P.-E. Pottie, A. Amy-Klein, Tackling the limits of optical fiber links. J. Opt. Soc. Am. B Opt. Phys. 32, 787 (2015)

    Article  ADS  Google Scholar 

  132. J. Geršl, P. Delva, P. Wolf, Relativistic corrections for time and frequency transfer in optical fibres. Metrologia 52, 552 (2015)

    Article  ADS  Google Scholar 

  133. P. Delva, J. Lodewyck, S. Bilicki, E. Bookjans, G. Vallet, R. Le Targat, P.-E. Pottie, C. Guerlin, F. Meynadier, C. Le Poncin-Lafitte, O. Lopez, A. Amy-Klein, W.-K. Lee, N. Quintin, C. Lisdat, A. Al-Masoudi, S. Dörscher, C. Grebing, G. Grosche, A. Kuhl, S. Raupach, U. Sterr, I.R. Hill, R. Hobson, W. Bowden, J. Kronjäger, G. Marra, A. Rolland, F.N. Baynes, H.S. Margolis, P. Gill, Test of special relativity using a fiber network of optical clocks. Phys. Rev. Lett. 118(22), 221102 (2017)

    Article  ADS  Google Scholar 

  134. D. Colladay, V.A. Kostelecký, CPT violation and the standard model. Phys. Rev. D 55, 6760–6774 (1997)

    Article  ADS  Google Scholar 

  135. D. Colladay, V.A. Kostelecký, Lorentz-violating extension of the standard model. Phys. Rev. D 58(11), 116002 (1998)

    Article  ADS  Google Scholar 

  136. V.A. Kostelecký, M. Mewes, Signals for Lorentz violation in electrodynamics. Phys. Rev. D 66(5), 056005 (2002)

    Article  ADS  Google Scholar 

  137. J.D. Tasson, What do we know about Lorentz invariance? Rep. Prog. Phys. 77(6), 062901 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  138. V.A. Kostelecký, N. Russell, Data tables for Lorentz and CPT violation. Rev. Mod. Phys. 83, 11–32 (2011)

    Article  ADS  Google Scholar 

  139. H. Pihan-Le Bars, C. Guerlin, R.-D. Lasseri, J.-P. Ebran, Q.G. Bailey, S. Bize, E. Khan, P. Wolf, Lorentz-symmetry test at Planck-scale suppression with nucleons in a spin-polarized \(^{133}\)Cs cold atom clock. Phys. Rev. D 95(7), 075026 (2017)

    Google Scholar 

  140. P. Wolf, F. Chapelet, S. Bize, A. Clairon, Cold atom clock test of Lorentz invariance in the matter sector. Phys. Rev. Lett. 96(6), 060801 (2006)

    Article  ADS  Google Scholar 

  141. M.A. Hohensee, S. Chu, A. Peters, H. Müller, Equivalence principle and gravitational redshift. Phys. Rev. Lett. 106(15), 151102 (2011)

    Article  ADS  Google Scholar 

  142. M.A. Hohensee, N. Leefer, D. Budker, C. Harabati, V.A. Dzuba, V.V. Flambaum, Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium. Phys. Rev. Lett. 111(5), 050401 (2013)

    Article  ADS  Google Scholar 

  143. T. Damour, Theoretical aspects of the equivalence principle. Class. Quantum Gravity 29(18), 184001 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  144. J.-P. Uzan, Varying constants, gravitation and cosmology. Living Rev. Relativ. 14, 2 (2011)

    Article  ADS  MATH  Google Scholar 

  145. J. Guéna, M. Abgrall, D. Rovera, P. Rosenbusch, M.E. Tobar, P. Laurent, A. Clairon, S. Bize, Improved tests of local position invariance using Rb87 and Cs133 fountains. Phys. Rev. Lett. 109(8), 080801 (2012)

    Article  ADS  Google Scholar 

  146. T. Rosenband, D.B. Hume, P.O. Schmidt, C.W. Chou, A. Brusch, L. Lorini, W.H. Oskay, R.E. Drullinger, T.M. Fortier, J.E. Stalnaker, S.A. Diddams, W.C. Swann, N.R. Newbury, W.M. Itano, D.J. Wineland, J.C. Bergquist, Frequency ratio of Al\(^{+}\) and Hg\(^{+}\) single-ion optical clocks; metrology at the 17th decimal place. Science 319, 1808– (2008)

    Article  ADS  Google Scholar 

  147. N. Leefer, C.T.M. Weber, A. Cingöz, J.R. Torgerson, D. Budker, New limits on variation of the fine-structure constant using atomic dysprosium. Phys. Rev. Lett. 111(6), 060801 (2013)

    Article  ADS  Google Scholar 

  148. R.M. Godun, P.B.R. Nisbet-Jones, J.M. Jones, S.A. King, L.A.M. Johnson, H.S. Margolis, K. Szymaniec, S.N. Lea, K. Bongs, P. Gill, Frequency ratio of two optical clock transitions in \(^{171}{\rm Yb}^{+}\) and constraints on the time variation of fundamental constants. Phys. Rev. Lett. 113(21), 210801 (2014)

    Article  ADS  Google Scholar 

  149. N. Huntemann, B. Lipphardt, C. Tamm, V. Gerginov, S. Weyers, E. Peik, Improved limit on a temporal variation of m\(_{p}\)/m\(_{e}\) from comparisons of Yb\(^{+}\) and Cs atomic clocks. Phys. Rev. Lett. 113(21), 210802 (2014)

    Article  ADS  Google Scholar 

  150. P. Brax, C. Burrage, A.-C. Davis, G. Gubitosi, Cosmological tests of the disformal coupling to radiation. J. Cosmol. Astropart. Phys. 11, 1 (2013)

    Article  ADS  Google Scholar 

  151. A. Hees, O. Minazzoli, J. Larena, Breaking of the equivalence principle in the electromagnetic sector and its cosmological signatures. Phys. Rev. D 90(12), 124064 (2014)

    Article  ADS  Google Scholar 

  152. R.F.L. Holanda, K.N.N.O. Barros, Searching for cosmological signatures of the Einstein equivalence principle breaking. Phys. Rev. D 94(2), 023524 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  153. S. Peil, S. Crane, J.L. Hanssen, T.B. Swanson, C.R. Ekstrom, Tests of local position invariance using continuously running atomic clocks. Phys. Rev. A 87(1), 010102 (2013)

    Article  ADS  Google Scholar 

  154. N. Ashby, T.P. Heavner, S.R. Jefferts, T.E. Parker, A.G. Radnaev, Y.O. Dudin, Testing local position invariance with four cesium-fountain primary frequency standards and four NIST hydrogen masers. Phys. Rev. Lett. 98(7), 070802 (2007)

    Article  ADS  Google Scholar 

  155. R.V. Pound, G.A. Rebka, Gravitational red-shift in nuclear resonance. Phys. Rev. Lett. 3, 439–441 (1959)

    Article  ADS  Google Scholar 

  156. R.F.C. Vessot, M.W. Levine, E.M. Mattison, E.L. Blomberg, T.E. Hoffman, G.U. Nystrom, B.F. Farrel, R. Decher, P.B. Eby, C.R. Baugher, Test of relativistic gravitation with a space-borne hydrogen maser. Phys. Rev. Lett. 45, 2081–2084 (1980)

    Article  ADS  Google Scholar 

  157. P. Delva, A. Hees, S. Bertone, E. Richard, P. Wolf, Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6. Class. Quantum Gravity 32(23), 232003 (2015)

    Article  ADS  Google Scholar 

  158. L. Cacciapuoti, C. Salomon, Atomic clock ensemble in space. J. Phys. Conf. Ser. 327(1), 012049 (2011)

    Article  Google Scholar 

  159. M. Soffel, H. Herold, H. Ruder, M. Schneider, Relativistic theory of gravimetric measurements and definition of thegeoid. Manuscr. Geod. 13, 143–146 (1988)

    ADS  Google Scholar 

  160. S.M. Kopejkin, Relativistic Manifestations of gravitational fields in gravimetry and geodesy. Manuscripta Geodaetica 16 (1991)

    Google Scholar 

  161. J. Müller, M. Soffel, S.A. Klioner, Geodesy and relativity. J. Geodesy 82, 133–145 (2008)

    Article  ADS  MATH  Google Scholar 

  162. P. Delva, J. Lodewyck, Atomic clocks: new prospects in metrology and geodesy. Acta Futura, (7), 67–78, 7:67–78, November 2013

    Google Scholar 

  163. B. Altschul, Q.G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J.D. Tasson, G.M. Tino, P. Tuckey, P. Wolf, Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission. Adv. Space Res. 55, 501–524 (2015)

    Article  ADS  Google Scholar 

  164. S. Zucker, T. Alexander, S. Gillessen, F. Eisenhauer, R. Genzel, Probing post-Newtonian physics near the galactic black hole with stellar redshift measurements. ApJl 639, L21–L24 (2006)

    Article  ADS  Google Scholar 

  165. M. Grould, F.H. Vincent, T. Paumard, G. Perrin, General relativistic effects on the orbit of the S2 star with GRAVITY. ArXiv e-prints (2017)

    Google Scholar 

  166. Gravity Collaboration, R. Abuter, A. Amorim, N. Anugu, M. Bauböck, M. Benisty, J. P. Berger, N. Blind, H. Bonnet, W. Brandner, A. Buron, C. Collin, F. Chapron, Y. Clénet, V. Coudé Du Foresto, P. T. de Zeeuw, C. Deen, F. Delplancke-Ströbele, R. Dembet, J. Dexter, G. Duvert, A. Eckart, F. Eisenhauer, G. Finger, N. M. Förster Schreiber, P. Fédou, P. Garcia, R. Garcia Lopez, F. Gao, E. Gendron, R. Genzel, S. Gillessen, P. Gordo, M. Habibi, X. Haubois, M. Haug, F. Haußmann, T. Henning, S. Hippler, M. Horrobin, Z. Hubert, N. Hubin, A. Jimenez Rosales, L. Jochum, K. Jocou, A. Kaufer, S. Kellner, S. Kendrew, P. Kervella, Y. Kok, M. Kulas, S. Lacour, V. Lapeyrère, B. Lazareff, J.-B. Le Bouquin, P. Léna, M. Lippa, R. Lenzen, A. Mérand, E. Müler, U. Neumann, T. Ott, L. Palanca, T. Paumard, L. Pasquini, K. Perraut, G. Perrin, O. Pfuhl, P. M. Plewa, S. Rabien, A. Ramírez, J. Ramos, C. Rau, G. Rodríguez-Coira, R.-R. Rohloff, G. Rousset, J. Sanchez-Bermudez, S. Scheithauer, M. Schöller, N. Schuler, J. Spyromilio, O. Straub, C. Straubmeier, E. Sturm, L. J. Tacconi, K. R. W. Tristram, F. Vincent, S. von Fellenberg, I. Wank, I. Waisberg, F. Widmann, E. Wieprecht, M. Wiest, E. Wiezorrek, J. Woillez, S. Yazici, D. Ziegler, and G. Zins. Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole. A&A 615, L15 (2018)

    Google Scholar 

  167. S. Weinberg, A new light boson? Phys. Rev. Lett. 40, 223–226 (1978)

    Article  ADS  Google Scholar 

  168. J. Preskill, M.B. Wise, F. Wilczek, Cosmology of the invisible axion. Phys. Lett. B 120, 127–132 (1983)

    Article  ADS  Google Scholar 

  169. W. Hu, R. Barkana, A. Gruzinov, Fuzzy cold dark matter: the wave properties of ultralight particles. Phys. Rev. Lett. 85, 1158–1161 (2000)

    Article  ADS  Google Scholar 

  170. F. Piazza, M. Pospelov, Sub-eV scalar dark matter through the super-renormalizable Higgs portal. Phys. Rev. D 82(4), 043533 (2010)

    Article  ADS  Google Scholar 

  171. A. Khmelnitsky, V. Rubakov, Pulsar timing signal from ultralight scalar dark matter. J. Cosmol. Astropart. Phys. 2, 019 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  172. N.K. Porayko, K.A. Postnov, Constraints on ultralight scalar dark matter from pulsar timing. Phys. Rev. D 90(6), 062008 (2014)

    Article  ADS  Google Scholar 

  173. H.-Y. Schive, T. Chiueh, T. Broadhurst, Cosmic structure as the quantum interference of a coherent dark wave. Nat. Phys. 10, 496–499 (2014)

    Article  Google Scholar 

  174. J. Beyer, C. Wetterich, Small scale structures in coupled scalar field dark matter. Phys. Lett. B 738, 418–423 (2014)

    Article  ADS  Google Scholar 

  175. A. Arvanitaki, J. Huang, K. Van Tilburg, Searching for dilaton dark matter with atomic clocks. Phys. Rev. D 91(1), 015015 (2015)

    Article  ADS  Google Scholar 

  176. Y.V. Stadnik, V.V. Flambaum, Searching for dark matter and variation of fundamental constants with laser and maser interferometry. Phys. Rev. Lett. 114(16), 161301 (2015)

    Article  ADS  Google Scholar 

  177. Y.V. Stadnik, V.V. Flambaum, Can dark matter induce cosmological evolution of the fundamental constants of nature? Phys. Rev. Lett. 115(20), 201301 (2015)

    Article  ADS  Google Scholar 

  178. P.W. Graham, D.E. Kaplan, J. Mardon, S. Rajendran, W.A. Terrano, Dark matter direct detection with accelerometers. Phys. Rev. D 93(7), 075029 (2016)

    Article  ADS  Google Scholar 

  179. A. Arvanitaki, S. Dimopoulos, K. Van Tilburg, Sound of dark matter: searching for light scalars with resonant-mass detectors. Phys. Rev. Lett. 116(3), 031102 (2016)

    Article  ADS  Google Scholar 

  180. Y.V. Stadnik, V.V. Flambaum, Enhanced effects of variation of the fundamental constants in laser interferometers and application to dark-matter detection. Phys. Rev. A 93(6), 063630 (2016)

    Article  ADS  Google Scholar 

  181. Y.V. Stadnik, V.V. Flambaum, Improved limits on interactions of low-mass spin-0 dark matter from atomic clock spectroscopy. Phys. Rev. A 94(2), 022111 (2016)

    Article  ADS  Google Scholar 

  182. D.J.E. Marsh, Axion cosmology. Phys. Rep. 643, 1–79 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  183. L.A. Ureña-López, A.X. Gonzalez-Morales, Towards accurate cosmological predictions for rapidly oscillating scalar fields as dark matter. J. Cosmol. Astropart. Phys. 7, 048 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  184. E. Calabrese, D.N. Spergel, Ultra-light dark matter in ultra-faint dwarf galaxies. MNRAS 460, 4397–4402 (2016)

    Article  ADS  Google Scholar 

  185. D. Blas, D.L. Nacir, S. Sibiryakov, Ultralight dark matter resonates with binary pulsars. Phys. Rev. Lett. 118(26), 261102 (2017)

    Article  ADS  Google Scholar 

  186. T. Bernal, V.H. Robles, T. Matos, Scalar field dark matter in clusters of galaxies. MNRAS 468, 3135–3149 (2017)

    Article  ADS  Google Scholar 

  187. L. Hui, J.P. Ostriker, S. Tremaine, E. Witten, Ultralight scalars as cosmological dark matter. Phys. Rev. D 95(4), 043541 (2017)

    Article  ADS  Google Scholar 

  188. C. Abel, N.J. Ayres, G. Ban, G. Bison, K. Bodek, V. Bondar, M. Daum, M. Fairbairn, V.V. Flambaum, P. Geltenbort, K. Green, W.C. Griffith, M. van der Grinten, Z.D. Grujić, P.G. Harris, N. Hild, P. Iaydjiev, S.N. Ivanov, M. Kasprzak, Y. Kermaidic, K. Kirch, H.-C. Koch, S. Komposch, P.A. Koss, A. Kozela, J. Krempel, B. Lauss, T. Lefort, Y. Lemière, D.J.E. Marsh, P. Mohanmurthy, A. Mtchedlishvili, M. Musgrave, F.M. Piegsa, G. Pignol, M. Rawlik, D. Rebreyend, D. Ries, S. Roccia, D. Rozpȩdzik, P. Schmidt-Wellenburg, N. Severijns, D. Shiers, Y.V. Stadnik, A. Weis, E. Wursten, J. Zejma, G. Zsigmond, Search for axion-like dark matter through nuclear spin precession in electric and magnetic fields. Phys. Rev. X 7(4), 041034 (2017)

    Google Scholar 

  189. T. Bernal, L.M. Fernández-Hernández, T. Matos, M.A. Rodríguez-Meza, Rotation curves of high-resolution LSB and SPARC galaxies with fuzzy and multistate (ultralight boson) scalar field dark matter. MNRAS 475, 1447–1468 (2018)

    Article  ADS  Google Scholar 

  190. M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory (1988)

    Google Scholar 

  191. T. Damour, A.M. Polyakov, The string dilation and a least coupling principle. Nucl. Phys. B 423, 532–558 (1994)

    Article  ADS  MATH  Google Scholar 

  192. T. Damour, A.M. Polyakov, String theory and gravity. Gen. Relativ. Gravit. 26, 1171–1176 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  193. M. Gasperini, F. Piazza, G. Veneziano, Quintessence as a runaway dilaton. Phys. Rev. D 65(2), 023508 (2001)

    Article  ADS  Google Scholar 

  194. T. Damour, F. Piazza, G. Veneziano, Runaway dilaton and equivalence principle violations. Phys. Rev. Lett. 89(8), 081601 (2002)

    Article  ADS  Google Scholar 

  195. T. Damour, J.F. Donoghue, Equivalence principle violations and couplings of a light dilaton. Phys. Rev. D 82(8), 084033 (2010)

    Article  ADS  Google Scholar 

  196. A. Hees, O. Minazzoli, E. Savalle, Y.V. Stadnik, P. Wolf, Violation of the equivalence principle from light scalar dark matter. Phys. Rev. D 98(6), 064051 (2018)

    Article  ADS  Google Scholar 

  197. A. Hees, J. Guéna, M. Abgrall, S. Bize, P. Wolf, Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons. Phys. Rev. Lett. 117(6), 061301 (2016)

    Article  ADS  Google Scholar 

  198. K. Van Tilburg, N. Leefer, L. Bougas, D. Budker, Search for ultralight scalar dark matter with atomic spectroscopy. Phys. Rev. Lett. 115(1), 011802 (2015)

    Article  ADS  Google Scholar 

  199. T.A. de Pirey Saint Alby, N. Yunes, Cosmological evolution and Solar System consistency of massive scalar-tensor gravity. Phys. Rev. D 96(6), 064040 (2017)

    Google Scholar 

  200. T. Damour, G. Esposito-Farese, Nonperturbative strong-field effects in tensor-scalar theories of gravitation. Phys. Rev. Lett. 70, 2220–2223 (1993)

    Article  ADS  Google Scholar 

  201. T. Damour, G. Esposito-Farèse, Tensor-scalar gravity and binary-pulsar experiments. Phys. Rev. D 54, 1474–1491 (1996)

    Article  ADS  Google Scholar 

  202. O. Minazzoli, A. Hees, Late-time cosmology of a scalar-tensor theory with a universal multiplicative coupling between the scalar field and the matter Lagrangian. Phys. Rev. D 90(2), 023017 (2014)

    Article  ADS  Google Scholar 

  203. S.M. Carroll, Quintessence and the rest of the world: suppressing long-range interactions. Phys. Rev. Lett. 81, 3067–3070 (1998)

    Article  ADS  Google Scholar 

  204. N.J. Nunes, J.E. Lidsey, Reconstructing the dark energy equation of state with varying alpha. Phys. Rev. D 69(12), 123511 (2004)

    Article  ADS  Google Scholar 

  205. C.J.A.P. Martins, A.M.M. Pinho, Fine-structure constant constraints on dark energy. Phys. Rev. D 91(10), 103501 (2015)

    Article  ADS  Google Scholar 

  206. M.A. Hohensee, H. Müller, R.B. Wiringa, Equivalence principle and bound kinetic energy. Phys. Rev. Lett. 111(15), 151102 (2013)

    Article  ADS  Google Scholar 

  207. H. Müller, S. Herrmann, A. Saenz, A. Peters, C. Lämmerzahl, Optical cavity tests of Lorentz invariance for the electron. Phys. Rev. D 68(11), 116006 (2003)

    Article  ADS  Google Scholar 

  208. H. Müller, Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators. Phys. Rev. D 71(4), 045004 (2005)

    Article  ADS  Google Scholar 

  209. N.A. Flowers, C. Goodge, J.D. Tasson, Superconducting-gravimeter tests of local lorentz invariance. Phys. Rev. Lett. 119(20), 201101 (2017)

    Article  ADS  Google Scholar 

  210. A. Bourgoin, C. Le Poncin-Lafitte, A. Hees, S. Bouquillon, G. Francou, M.-C. Angonin, Lorentz symmetry violations from matter-gravity couplings with lunar laser ranging. Phys. Rev. Lett. 119(20), 201102 (2017)

    Article  ADS  Google Scholar 

  211. H. Pihan-Le Bars, C. Guerlin, P. Wolf, Progress on testing Lorentz symmetry with MICROSCOPE. ArXiv e-prints (2017)

    Google Scholar 

  212. B. Bertotti, L. Iess, P. Tortora, A test of general relativity using radio links with the Cassini spacecraft. Nature 425, 374–376 (2003)

    Article  ADS  Google Scholar 

  213. S.B. Lambert, C. Le Poncin-Lafitte, Determining the relativistic parameter \(\gamma \) using very long baseline interferometry. A&A 499, 331–335 (2009)

    Article  ADS  MATH  Google Scholar 

  214. S.B. Lambert, C. Le Poncin-Lafitte, Improved determination of \(\gamma \) by VLBI. A&A 529, A70 (2011)

    Article  ADS  Google Scholar 

  215. A.S. Konopliv, S.W. Asmar, W.M. Folkner, Ö. Karatekin, D.C. Nunes, S.E. Smrekar, C.F. Yoder, M.T. Zuber, Mars high resolution gravity fields from mro, mars seasonal gravity, and other dynamical parameters. Icarus 211(1), 401–428 (2011)

    Article  ADS  Google Scholar 

  216. R.S. Park, W.M. Folkner, A.S. Konopliv, J.G. Williams, D.E. Smith, M.T. Zuber, Precession of mercury’s perihelion from ranging to the MESSENGER spacecraft. AJ 153, 121 (2017)

    Article  ADS  Google Scholar 

  217. E.G. Adelberger, B.R. Heckel, A.E. Nelson, Tests of the gravitational inverse-square law. Ann. Rev. Nucl. Part. Sci. 53, 77–121 (2003)

    Article  ADS  Google Scholar 

  218. P. Jordan, Formation of the stars and development of the universe. Nature 164, 637–640 (1949)

    Article  ADS  MATH  Google Scholar 

  219. C. Brans, R.H. Dicke, Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  220. T. Damour, G. Esposito-Farese, Tensor-multi-scalar theories of gravitation. Class. Quantum Gravity 9, 2093–2176 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  221. J. Khoury, A. Weltman, Chameleon cosmology. Phys. Rev. D 69(4), 044026 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  222. J. Khoury, A. Weltman, Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93(17), 171104 (2004)

    Article  ADS  Google Scholar 

  223. A. Hees, A. Füzfa, Combined cosmological and solar system constraints on chameleon mechanism. Phys. Rev. D 85(10), 103005 (2012)

    Article  ADS  Google Scholar 

  224. K. Hinterbichler, J. Khoury, Screening long-range forces through local symmetry restoration. Phys. Rev. Lett. 104(23), 231301 (2010)

    Article  ADS  Google Scholar 

  225. K. Hinterbichler, J. Khoury, A. Levy, A. Matas, Symmetron cosmology. Phys. Rev. D 84(10), 103521 (2011)

    Article  ADS  Google Scholar 

  226. A.I. Vainshtein, To the problem of nonvanishing gravitation mass. Phys. Lett. B 39, 393–394 (1972)

    Article  ADS  Google Scholar 

  227. E. Babichev, C. Deffayet, R. Ziour, The vainshtein mechanism in the decoupling limit of massive gravity. Jo. High Energy Phys. 5, 98 (2009)

    Article  ADS  MATH  Google Scholar 

  228. E. Babichev, C. Deffayet, R. Ziour, k-MOUFLAGE gravity. Int. J. Mod. Phys. D 18, 2147–2154 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  229. E. Babichev, C. Deffayet, G. Esposito-Farèse, Constraints on shift-symmetric scalar-tensor theories with a vainshtein mechanism from bounds on the time variation of G. Phys. Rev. Lett. 107(25), 251102 (2011)

    Article  ADS  Google Scholar 

  230. F. Hofmann, J. Müller, Relativistic tests with lunar laser ranging. Class. Quantum Gravity 35(3), 035015 (2018)

    Article  ADS  MATH  Google Scholar 

  231. M.D. Seifert, Vector models of gravitational Lorentz symmetry breaking. Phys. Rev. D 79(12), 124012 (2009)

    Article  ADS  Google Scholar 

  232. V.A. Kostelecký, R. Potting, Gravity from local Lorentz violation. Gen. Relativ. Gravit. 37, 1675–1679 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  233. V.A. Kostelecký, R. Potting, Gravity from spontaneous Lorentz violation. Phys. Rev. D 79(6), 065018 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  234. B. Altschul, Q.G. Bailey, V.A. Kostelecký, Lorentz violation with an antisymmetric tensor. Phys. Rev. D 81(6), 065028 (2010)

    Article  ADS  Google Scholar 

  235. R. Gambini, J. Pullin, Nonstandard optics from quantum space-time. Phys. Rev. D 59(12), 124021 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  236. V.A. Kostelecký, M. Mewes, Electrodynamics with Lorentz-violating operators of arbitrary dimension. Phys. Rev. D 80(1), 015020 (2009)

    Article  ADS  Google Scholar 

  237. S.M. Carroll, J.A. Harvey, V.A. Kostelecký, C.D. Lane, T. Okamoto, Noncommutative field theory and Lorentz violation. Phys. Rev. Lett. 87(14), 141601 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  238. V.A. Kostelecký, R. Lehnert, Stability, causality, and Lorentz and CPT violation. Phys. Rev. D 63(6), 065008 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  239. Q.G. Bailey, V.A. Kostelecký, R. Xu, Short-range gravity and Lorentz violation. Phys. Rev. D 91(2), 022006 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  240. V.A. Kostelecký, J.D. Tasson, Constraints on Lorentz violation from gravitational Čerenkov radiation. Phys. Lett. B 749, 551–559 (2015)

    Article  ADS  Google Scholar 

  241. V.A. Kostelecký, M. Mewes, Testing local Lorentz invariance with gravitational waves. Phys. Lett. B 757, 510–514 (2016)

    Article  ADS  MATH  Google Scholar 

  242. Q.G. Bailey, D. Havert, Velocity-dependent inverse cubic force and solar system gravity tests. Phys. Rev. D 96(6), 064035 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  243. H. Müller, S.-W. Chiow, S. Herrmann, S. Chu, K.-Y. Chung, Atom-interferometry tests of the isotropy of post-Newtonian gravity. Phys. Rev. Lett. 100(3), 031101 (2008)

    Article  ADS  Google Scholar 

  244. K.-Y. Chung, S.-W. Chiow, S. Herrmann, S. Chu, H. Müller, Atom interferometry tests of local Lorentz invariance in gravity and electrodynamics. Phys. Rev. D 80(1), 016002 (2009)

    Article  ADS  Google Scholar 

  245. C.-G. Shao, Y.-F. Chen, R. Sun, L.-S. Cao, M.-K. Zhou, Z.-K. Hu, C. Yu, H. Müller, Limits on Lorentz violation in gravity from worldwide superconducting gravimeters. Phys. Rev. D 97(2), 024019 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  246. A. Hees, Q.G. Bailey, C. Le Poncin-Lafitte, A. Bourgoin, A. Rivoldini, B. Lamine, F. Meynadier, C. Guerlin, P. Wolf, Testing Lorentz symmetry with planetary orbital dynamics. Phys. Rev. D 92, 064049 (2015)

    Article  ADS  Google Scholar 

  247. C. Le Poncin-Lafitte, A. Hees, S. lambert, Lorentz symmetry and very long baseline interferometry. Phys. Rev. D 94(12), 125030 (2016)

    Google Scholar 

  248. J.B.R. Battat, J.F. Chandler, C.W. Stubbs, Testing for Lorentz violation: constraints on standard-model-extension parameters via lunar laser ranging. Phys. Rev. Lett. 99(24), 241103 (2007)

    Article  ADS  Google Scholar 

  249. A. Bourgoin, A. Hees, S. Bouquillon, C. Le Poncin-Lafitte, G. Francou, M.-C. Angonin, Testing Lorentz symmetry with lunar laser ranging. Phys. Rev. Lett. 117(24), 241301 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  250. M. Milgrom, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. ApJ 270, 365–370 (1983)

    Article  ADS  Google Scholar 

  251. M. Milgrom, A modification of the Newtonian dynamics - implications for galaxy systems. ApJ 270, 384 (1983)

    Article  ADS  Google Scholar 

  252. M. Milgrom, A modification of the Newtonian dynamics - implications for galaxies. ApJ 270, 371–389 (1983)

    Article  ADS  Google Scholar 

  253. J.-P. Bruneton, G. Esposito-Farèse, Field-theoretical formulations of MOND-like gravity. Phys. Rev. D 76(12), 124012 (2007)

    Article  ADS  Google Scholar 

  254. A. Hees, B. Famaey, G.W. Angus, G. Gentile, Combined solar system and rotation curve constraints on MOND. MNRAS 455, 449–461 (2016)

    Article  ADS  Google Scholar 

  255. R.A. Swaters, R.H. Sanders, S.S. McGaugh, Testing modified Newtonian dynamics with rotation curves of dwarf and low surface brightness galaxies. ApJ 718, 380–391 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aurélien Hees .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hees, A., Bourgoin, A., Delva, P., Le Poncin-Lafitte, C., Wolf, P. (2019). Use of Geodesy and Geophysics Measurements to Probe the Gravitational Interaction. In: Puetzfeld, D., Lämmerzahl, C. (eds) Relativistic Geodesy. Fundamental Theories of Physics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-030-11500-5_9

Download citation

Publish with us

Policies and ethics