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Parametrized Post-Newtonian Formalism

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Abstract

The parametrized post-Newtonian (PPN) formalism is an indispensable tool for assessing the viability of gravity theories. Its virtue is to separate this task, which comprises the comparison of the predictions of a given theory of gravity to observations, into two independent parts: the derivation of a number of parameter values from any given theory of gravity, and the measurement of these values by Solar System observations. Since its original development more than a century ago, the PPN formalism has undergone several extensions, and been applied to a vast number of gravity theories. This chapter gives an overview of the PPN formalism, the necessary assumptions imposed on the gravity theories under investigation, and its extensions.

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Notes

  1. 1.

    Assuming \(6\zeta _4 = 3\alpha _3 + 2\zeta _1 - 3\zeta _3\) [20].

References

  1. A.S. Eddington, The Mathematical Theory of Relativity (Cambridge University Press, Cambridge, 1922)

    MATH  Google Scholar 

  2. H.P. Robertson, Relativity and cosmology, in Space Age Astronomy. ed. by A.J. Deutsch, W.B. Klemperer (1962), p. 228

    Google Scholar 

  3. L.I. Schiff, Comparison of theory and observation in general relativity, in Relativity Theory and Astrophysics. Vol. 1: Relativity and Cosmology. ed. by J. Ehlers (1967), p. 105

    Google Scholar 

  4. R. Baierlein, Testing general relativity with laser ranging to the moon. Phys. Rev. 162, 1275–1288 (1967)

    Article  ADS  Google Scholar 

  5. K. Nordtvedt, Equivalence principle for massive bodies. 1. Phenomenology. Phys. Rev. 169, 1014–1016 (1968)

    Article  ADS  Google Scholar 

  6. K. Nordtvedt, Equivalence principle for massive bodies. 2. Theory. Phys. Rev. 169, 1017–1025 (1968)

    Article  ADS  Google Scholar 

  7. K.S. Thorne, C.M. Will, Theoretical frameworks for testing relativistic gravity. I. Foundations. Astrophys. J. 163, 595–610 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  8. C.M. Will, Theoretical frameworks for testing relativistic gravity. 2. Parametrized post-Newtonian hydrodynamics, and the Nordtvedt effect. Astrophys. J. 163, 611–627 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  9. C.M. Will, Theoretical frameworks for testing relativistic gravity. 3. Conservation laws, Lorentz invariance and values of the PPN parameters. Astrophys. J. 169, 125–140 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  10. C.M. Will, K. Nordtvedt Jr., Conservation laws and preferred frames in relativistic gravity. I. Preferred-frame theories and an extended PPN formalism. Astrophys. J. 177, 757 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  11. K.J. Nordtvedt, C.M. Will, Conservation laws and preferred frames in relativistic gravity. II. Experimental evidence to rule out preferred-frame theories of gravity. Astrophys. J. 177, 775–792 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  12. C.M. Will, Relativistic gravity in the solar system. III. Experimental disproof of a class of linear theories of gravitation. Astrophys. J. 185, 31–42 (1973)

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  14. 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 

  15. E. Fomalont, S. Kopeikin, G. Lanyi, J. Benson, Progress in measurements of the gravitational bending of radio waves using the VLBA. Astrophys. J. 699, 1395–1402 (2009). (arXiv:0904.3992)

    Article  ADS  Google Scholar 

  16. A. Verma, A. Fienga, J. Laskar, H. Manche, M. Gastineau, Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity. Astron. Astrophys. 561, A115 (2014). (arXiv:1306.5569)

    Article  ADS  Google Scholar 

  17. V. Viswanathan, A. Fienga, M. Gastineau, J. Laskar, INPOP17a planetary ephemerides, Notes Scientifiques et Techniques de l’Institut de Mecanique Celeste 108 (2017)

    Google Scholar 

  18. V. Viswanathan, A. Fienga, O. Minazzoli, L. Bernus, J. Laskar, M. Gastineau, The new lunar ephemeris INPOP17a and its application to fundamental physics. Mon. Not. Roy. Astron. Soc. 476(2), 1877–1888 (2018). arXiv:1710.09167

  19. L.B. Kreuzer, Experimental measurement of the equivalence of active and passive gravitational mass. Phys. Rev. 169, 1007–1012 (1968)

    Article  ADS  Google Scholar 

  20. C.M. Will, Active mass in relativistic gravity - theoretical interpretation of the Kreuzer experiment. Astrophys. J. 204, 224–234 (1976)

    Article  ADS  Google Scholar 

  21. C.M. Will, The confrontation between general relativity and experiment. Living Rev. Rel. 17, 4 (2014). (arXiv:1403.7377)

    Article  Google Scholar 

  22. C.M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 2018)

    Google Scholar 

  23. P. Horava, Quantum gravity at a Lifshitz point. Phys. Rev. D 79, 084008 (2009). arXiv:0901.3775

  24. K. Lin, S. Mukohyama, A. Wang, Solar system tests and interpretation of gauge field and Newtonian prepotential in general covariant Hořava-Lifshitz gravity. Phys. Rev. D 86, 104024 (2012). arXiv:1206.1338

  25. K. Lin, A. Wang, Static post-Newtonian limits in nonprojectable Hořava-Lifshitz gravity with an extra U(1) symmetry. Phys. Rev. D87(8), 084041 (2013). arXiv:1212.6794

  26. K. Lin, S. Mukohyama, A. Wang, T. Zhu, Post-Newtonian approximations in the Hořava-Lifshitz gravity with extra U(1) symmetry. Phys. Rev. D89(8), 084022 (2014). arXiv:1310.6666

  27. H.W. Zaglauer, Phenomenological aspects of scalar fields in astrophysics, cosmology and particle physics. Ph.D. thesis, Washington U., St. Louis (1990)

    Google Scholar 

  28. T. Helbig, Gravitational effects of light scalar particles. Astrophys. J. 382, 223–232 (1991)

    Article  ADS  Google Scholar 

  29. M.S. Gladchenko, V.N. Ponomarev, V.V. Zhytnikov, PPN metric and PPN torsion in the quadratic Poincare gauge theory of gravity. Phys. Lett. B 241, 67–69 (1990)

    Article  ADS  Google Scholar 

  30. S. Alexander, N. Yunes, A New PPN parameter to test Chern-Simons gravity. Phys. Rev. Lett. 99, 241101 (2007). [hep-th/0703265]

    Google Scholar 

  31. S. Alexander, N. Yunes, Parametrized post-Newtonian expansion of Chern-Simons gravity. Phys. Rev. D 75, 124022 (2007). arXiv:0704.0299

  32. S. Alexander, N. Yunes, Chern-Simons modified general relativity. Phys. Rept. 480, 1–55 (2009). arXiv:0907.2562

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

    Article  ADS  Google Scholar 

  34. E. Babichev, C. Deffayet, An introduction to the Vainshtein mechanism. Class. Quant. Grav. 30, 184001 (2013). arXiv:1304.7240

  35. A. Avilez-Lopez, A. Padilla, P.M. Saffin, C. Skordis, The parametrized post-Newtonian-Vainshteinian formalism. JCAP 1506(06), 044 (2015). arXiv:1501.01985

  36. J. Khoury, A. Weltman, Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93, 171104 (2004). [astro-ph/0309300]

    Google Scholar 

  37. A. Hees, A. Fuzfa, Combined cosmological and solar system constraints on chameleon mechanism. Phys. Rev. D 85, 103005 (2012). arXiv:1111.4784

  38. A. Schärer, R. Angélil, R. Bondarescu, P. Jetzer, A. Lundgren, Testing scalar-tensor theories and parametrized post-Newtonian parameters in Earth orbit. Phys. Rev. D90(12), 123005 (2014). arXiv:1410.7914

  39. C. Burrage, J. Sakstein, A compendium of chameleon constraints. JCAP 1611(11), 045 (2016). arXiv:1609.01192

  40. C. Burrage, J. Sakstein, Tests of chameleon gravity. Living Rev. Rel. 21(1), 1 (2018). arXiv:1709.09071

  41. R. McManus, L. Lombriser, J. Peñarrubia, Parameterised post-Newtonian expansion in screened regions. JCAP 1712(12), 031 (2017). arXiv:1705.05324

  42. V.A.A. Sanghai, T. Clifton, Parameterized post-Newtonian cosmology. Class. Quant. Grav. 34(6), 065003 (2017). arXiv:1610.08039

  43. N. Rosen, A theory of gravitation. Ann. Phys. 84, 455–473 (1974)

    Article  ADS  Google Scholar 

  44. D.L. Lee, C.M. Caves, W.-T. Ni, C.M. Will, Theoretical frameworks for testing relativistic gravity. 5. Post Newtonian limit of Rosen’s theory. Astrophys. J. 206, 555–558 (1976)

    Google Scholar 

  45. K. Hinterbichler, Theoretical aspects of massive gravity. Rev. Mod. Phys. 84, 671–710 (2012). arXiv:1105.3735

  46. C. de Rham, Massive gravity. Living Rev. Rel. 17, 7 (2014). arXiv:1401.4173

  47. T. Clifton, M. Banados, C. Skordis, The parameterised post-Newtonian limit of bimetric theories of gravity. Class. Quant. Grav. 27, 235020 (2010). arXiv:1006.5619

  48. M. Hohmann, M.N.R. Wohlfarth, Multimetric extension of the PPN formalism: experimental consistency of repulsive gravity. Phys. Rev. D 82, 084028 (2010). arXiv:1007.4945

  49. M. Hohmann, Parameterized post-Newtonian formalism for multimetric gravity. Class. Quant. Grav. 31, 135003 (2014). arXiv:1309.7787

  50. L.L. Smalley, Postnewtonian approximation of the Poincare gauge theory of gravitation. Phys. Rev. D 21, 328–331 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  51. J. Nitsch, F.W. Hehl, Translational Gauge theory of gravity: post Newtonian approximation and spin precession. Phys. Lett. 90B, 98–102 (1980)

    Article  ADS  Google Scholar 

  52. J. Hayward, Scalar tetrad theories of gravity. Gen. Rel. Grav. 13, 43–55 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  53. U. Ualikhanova, M. Hohmann, Parameterized post-Newtonian limit of general teleparallel gravity theories. arXiv:1907.08178

  54. J.M. Bardeen, Gauge invariant cosmological perturbations. Phys. Rev. D 22, 1882–1905 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  55. H. Kodama, M. Sasaki, Cosmological perturbation theory. Prog. Theor. Phys. Suppl. 78, 1–166 (1984)

    Article  ADS  Google Scholar 

  56. V.F. Mukhanov, H.A. Feldman, R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions. Phys. Rept. 215, 203–333 (1992)

    Google Scholar 

  57. K.A. Malik, D. Wands, Cosmological perturbations. Phys. Rept. 475, 1–51 (2009). arXiv:0809.4944

  58. K. Nakamura, Second-order gauge invariant cosmological perturbation theory: Einstein equations in terms of gauge invariant variables. Prog. Theor. Phys. 117, 17–74 (2007). [gr-qc/0605108]

    Google Scholar 

  59. K. Nakamura, Gauge-invariant formulation of the second-order cosmological perturbations. Phys. Rev. D 74, 101301 (2006). [gr-qc/0605107]

    Google Scholar 

  60. M. Hohmann, Gauge-invariant approach to the parametrized post-Newtonian formalism. Phys. Rev. D 101(2), 024061 (2020). arXiv:1910.09245

  61. E.E. Flanagan, The Conformal frame freedom in theories of gravitation. Class. Quant. Grav. 21, 3817 (2004). [gr-qc/0403063]

    Google Scholar 

  62. K. Nordtvedt Jr., Post-Newtonian metric for a general class of scalar tensor gravitational theories and observational consequences. Astrophys. J. 161, 1059–1067 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  63. O. Minazzoli, B. Chauvineau, Scalar-tensor propagation of light in the inner solar system at the millimetric level. Class. Quant. Grav. 28, 085010 (2011). arXiv:1007.3942

  64. X.-M. Deng, Y. Xie, Two-post-Newtonian light propagation in the scalar-tensor theory: an \(N\)-point-masses case. Phys. Rev. D 86, 044007 (2012). arXiv:1207.3138

  65. G.J. Olmo, The Gravity Lagrangian according to solar system experiments. Phys. Rev. Lett. 95, 261102 (2005). [gr-qc/0505101]

    Google Scholar 

  66. G.J. Olmo, Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism. Phys. Rev. D 72, 083505 (2005). [gr-qc/0505135]

    Google Scholar 

  67. L. Perivolaropoulos, PPN parameter gamma and solar system constraints of massive Brans-Dicke theories. Phys. Rev. D 81, 047501 (2010). arXiv:0911.3401

  68. Y. Xie, W.-T. Ni, P. Dong, T.-Y. Huang, Second post-Newtonian approximation of scalar-tensor theory of gravity. Adv. Space Res. 43, 171–180 (2009). arXiv:0704.2991

  69. M. Hohmann, L. Jarv, P. Kuusk, E. Randla, Post-Newtonian parameters \(\gamma \) and \(\beta \) of scalar-tensor gravity with a general potential. Phys. Rev. D88(8), 084054 (2013). arXiv:1309.0031. [Erratum: Phys. Rev. D89(6), 069901 (2014)]

  70. L. Järv, P. Kuusk, M. Saal, O. Vilson, Invariant quantities in the scalar-tensor theories of gravitation. Phys. Rev. D91(2), 024041 (2015). arXiv:1411.1947

  71. M. Hohmann, A. Schärer, Post-Newtonian parameters \(\gamma \) and \(\beta \) of scalar-tensor gravity for a homogeneous gravitating sphere. Phys. Rev. D96(10), 104026 (2017). arXiv:1708.07851

  72. J.W. Moffat, V.T. Toth, Modified Jordan-Brans-Dicke theory with scalar current and the Eddington-Robertson \(\gamma \)-parameter. Int. J. Mod. Phys. D 21, 1250084 (2012). arXiv:1001.1564

  73. K. Saaidi, A. Mohammadi, H. Sheikhahmadi, \(\gamma \) parameter and solar system constraint in Chameleon Brans Dick theory. Phys. Rev. D 83, 104019 (2011). arXiv:1201.0271

  74. O. Minazzoli, \(\gamma \) parameter and solar system constraint in scalar-tensor theory with a power law potential and universal scalar/matter coupling. arXiv:1208.2372

  75. N.C. Devi, S. Panda, A.A. Sen, Solar system constraints on scalar tensor theories with non-standard action. Phys. Rev. D 84, 063521 (2011). arXiv:1104.0152

  76. M. Roshan, F. Shojai, Notes on the post-Newtonian limit of massive Brans-Dicke theory. Class. Quant. Grav. 28, 145012 (2011). arXiv:1106.1264

  77. O. Minazzoli, A. Hees, Intrinsic solar system decoupling of a scalar-tensor theory with a universal coupling between the scalar field and the matter Lagrangian. Phys. Rev. D88(4), 041504 (2013). arXiv:1308.2770

  78. S. Capozziello, A. Troisi, PPN-limit of fourth order gravity inspired by scalar-tensor gravity. Phys. Rev. D 72, 044022 (2005). [astro-ph/0507545]

    Google Scholar 

  79. S. Capozziello, A. Stabile, A. Troisi, Fourth-order gravity and experimental constraints on Eddington parameters. Mod. Phys. Lett. A 21, 2291–2301 (2006). [gr-qc/0603071]

    Google Scholar 

  80. S. Capozziello, A. Stabile, A. Troisi, The Newtonian limit of f(R) gravity. Phys. Rev. D 76, 104019 (2007). arXiv:0708.0723

  81. S. Capozziello, A. Stabile, A. Troisi, Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit. Phys. Lett. B 686, 79–83 (2010). arXiv:1002.1364

  82. T. Clifton, The parameterised post-Newtonian limit of fourth-order theories of gravity. Phys. Rev. D 77, 024041 (2008). arXiv:0801.0983

  83. M. Capone, M.L. Ruggiero, Jumping from metric f(R) to scalar-tensor theories and the relations between their post-Newtonian Parameters. Class. Quant. Grav. 27, 125006 (2010). arXiv:0910.0434

  84. S. Capozziello, A. Stabile, The weak field limit of fourth order gravity, in Classical and Quantum Gravity: Theory and Applications* Chapter 2, ed. by *R. Frignanni, Vincent (2010). arXiv:1009.3441

  85. T. Harko, T.S. Koivisto, F.S.N. Lobo, G.J. Olmo, Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration. Phys. Rev. D 85, 084016 (2012). arXiv:1110.1049

  86. X.-M. Deng, Y. Xie, Solar System tests of a scalar-tensor gravity with a general potential: insensitivity of light deflection and Cassini tracking. Phys. Rev. D93(4), 044013 (2016)

    Google Scholar 

  87. X. Zhang, W. Zhao, H. Huang, Y. Cai, Post-Newtonian parameters and cosmological constant of screened modified gravity. Phys. Rev. D93(12), 124003 (2016). arXiv:1603.09450

  88. T. Damour, G. Esposito-Farese, Tensor multiscalar theories of gravitation. Class. Quant. Grav. 9, 2093–2176 (1992)

    Article  ADS  Google Scholar 

  89. A.L. Berkin, R.W. Hellings, Multiple field scalar - tensor theories of gravity and cosmology. Phys. Rev. D 49, 6442–6449 (1994). [gr-qc/9401033]

    Google Scholar 

  90. E. Randla, PPN parameters for multiscalar-tensor gravity without a potential. J. Phys. Conf. Ser. 532, 012024 (2014)

    Google Scholar 

  91. P. Kuusk, L. Jarv, O. Vilson, Invariant quantities in the multiscalar-tensor theories of gravitation. Int. J. Mod. Phys. A31(02n03), 1641003 (2016). arXiv:1509.02903

  92. M. Hohmann, L. Jarv, P. Kuusk, E. Randla, O. Vilson, Post-Newtonian parameter \(\gamma \) for multiscalar-tensor gravity with a general potential. Phys. Rev. D94(12), 124015 (2016). arXiv:1607.02356

  93. T.S. Koivisto, The post-Newtonian limit in C-theories of gravitation. Phys. Rev. D 84, 121502 (2011). arXiv:1109.4585

  94. T.S. Koivisto, Newtonian limit of nonlocal cosmology. Phys. Rev. D 78, 123505 (2008). arXiv:0807.3778

  95. A. Conroy, T. Koivisto, A. Mazumdar, A. Teimouri, Generalized quadratic curvature, non-local infrared modifications of gravity and Newtonian potentials. Class. Quant. Grav. 32(1), 015024 (2015). arXiv:1406.4998

  96. G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space. Int. J. Theor. Phys. 10, 363–384 (1974)

    Article  MathSciNet  Google Scholar 

  97. C. Deffayet, X. Gao, D. Steer, G. Zahariade, From k-essence to generalised Galileons. Phys. Rev. D 84, 064039 (2011). arXiv:1103.3260

  98. T. Kobayashi, M. Yamaguchi, J. Yokoyama, Generalized G-inflation: inflation with the most general second-order field equations. Prog. Theor. Phys. 126, 511–529 (2011). arXiv:1105.5723

  99. M. Hohmann, Parametrized post-Newtonian limit of Horndeski’s gravity theory. Phys. Rev. D92(6), 064019 (2015). arXiv:1506.04253

  100. S. Hou, Y. Gong, Constraints on Horndeski theory using the observations of Nordtvedt effect, Shapiro time delay and binary pulsars. Eur. Phys. J. C78(3), 247 (2018). arXiv:1711.05034

  101. R. Kase, S. Tsujikawa, Screening the fifth force in the Horndeski’s most general scalar-tensor theories. JCAP 1308, 054 (2013). arXiv:1306.6401

  102. C. de Rham, G. Gabadadze, A.J. Tolley, Resummation of massive gravity. Phys. Rev. Lett. 106, 231101 (2011). arXiv:1011.1232

  103. S. Hassan, R.A. Rosen, Bimetric gravity from ghost-free massive gravity. JHEP 1202, 126 (2012). arXiv:1109.3515

  104. K. Hinterbichler, R.A. Rosen, Interacting spin-2 fields. JHEP 1207, 047 (2012). arXiv:1203.5783

  105. A. Schmidt-May, M. von Strauss, Recent developments in bimetric theory. J. Phys. A49(18), 183001 (2016). arXiv:1512.00021

  106. M. Hohmann, Post-Newtonian parameter \(\gamma \) and the deflection of light in ghost-free massive bimetric gravity. Phys. Rev. D95(12), 124049 (2017). arXiv:1701.07700

  107. A. Einstein, Riemann-Geometrie mit Aufrechterhaltung des Begriffes des Fernparallelismus. Sitzber. Preuss. Akad. Wiss. 17, 217–221 (1928)

    MATH  Google Scholar 

  108. R. Aldrovandi, J.G. Pereira, Teleparallel Gravity, vol. 173 (Springer, Dordrecht, 2013)

    Book  Google Scholar 

  109. J.W. Maluf, The teleparallel equivalent of general relativity. Ann. Phys. 525, 339–357 (2013). arXiv:1303.3897

  110. J.B. Jiménez, L. Heisenberg, T.S. Koivisto, The geometrical trinity of gravity. Universe 5(7), 173 (2019). arXiv:1903.06830

  111. G.R. Bengochea, R. Ferraro, Dark torsion as the cosmic speed-up. Phys. Rev. D 79, 124019 (2009). arXiv:0812.1205

  112. E.V. Linder, Einstein’s other gravity and the acceleration of the universe. Phys. Rev. D 81, 127301 (2010). arXiv:1005.3039. [Erratum: Phys. Rev. D82, 109902 (2010)]

  113. K. Hayashi, T. Shirafuji, New general relativity. Phys. Rev. D19, 3524–3553 (1979) [409 (1979)]

    Google Scholar 

  114. S. Bahamonde, C.G. Böhmer, M. Krššák, New classes of modified teleparallel gravity models. Phys. Lett. B775, 37–43 (2017). arXiv:1706.04920

  115. . M. Krššák, E.N. Saridakis, The covariant formulation of f(T) gravity. Class. Quant. Grav. 33(11), 115009 (2016). arXiv:1510.08432

  116. M. Krssak, R.J. van den Hoogen, J.G. Pereira, C.G. Böhmer, A.A. Coley, Teleparallel theories of gravity: illuminating a fully invariant approach. Class. Quant. Grav. 36(18), 183001 (2019). arXiv:1810.12932

  117. M. Hohmann, L. Järv, U. Ualikhanova, Covariant formulation of scalar-torsion gravity. Phys. Rev. D97(10), 104011 (2018). arXiv:1801.05786

  118. M. Hohmann, Scalar-torsion theories of gravity I: general formalism and conformal transformations. Phys. Rev. D98(6), 064002 (2018). arXiv:1801.06528

  119. M. Hohmann, C. Pfeifer, Scalar-torsion theories of gravity II: \(L(T, X, Y, \phi )\) theory. Phys. Rev. D98(6), 064003 (2018). arXiv:1801.06536

  120. M. Hohmann, Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants. Phys. Rev. D98(6), 064004 (2018). arXiv:1801.06531

  121. J.-T. Li, Y.-P. Wu, C.-Q. Geng, Parametrized post-Newtonian limit of the teleparallel dark energy model. Phys. Rev. D89(4), 044040 (2014). arXiv:1312.4332

  122. Z.-C. Chen, Y. Wu, H. Wei, Post-Newtonian approximation of teleparallel gravity coupled with a scalar field. Nucl. Phys. B 894, 422–438 (2015). arXiv:1410.7715

  123. H. Mohseni Sadjadi, Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term. Eur. Phys. J. C77(3), 191 (2017). arXiv:1606.04362

  124. E.D. Emtsova, M. Hohmann, Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories. Phys. Rev. D 101(2), 024017 (2020). arXiv:1909.09355

  125. K. Flathmann, M. Hohmann, Post-Newtonian limit of generalized scalar-torsion theories of gravity. Phys. Rev. D 101(2), 024005 (2020). arXiv:1910.01023

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  1. Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411, Tartu, Estonia

    Manuel Hohmann

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  1. Manuel Hohmann
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Editors and Affiliations

  1. National Observatory of Athens, Athens, Greece

    Emmanuel N. Saridakis

  2. University of the Basque Country, Leioa, Spain

    Ruth Lazkoz

  3. Institute of Physics, University of Szczecin, Szczecin, Poland

    Vincenzo Salzano

  4. University of Beira Interior, Covilhã, Portugal

    Paulo Vargas Moniz

  5. Università di Napoli Federico II, Napoli, Italy

    Salvatore Capozziello

  6. University of Salamanca, Salamanca, Spain

    Jose Beltrán Jiménez

  7. University of Naples Federico II, Napoli, Italy

    Mariafelicia De Laurentis

  8. University of Valencia, Burjassot, Valencia, Spain

    Gonzalo J. Olmo

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Hohmann, M. (2021). Parametrized Post-Newtonian Formalism. In: Saridakis, E.N., et al. Modified Gravity and Cosmology. Springer, Cham. https://doi.org/10.1007/978-3-030-83715-0_24

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