Newtonian-like gravity with variable G

Abstract

We propose a Lagrangian formulation for a varying G Newtonian-like theory inspired by the Brans–Dicke gravity. Rather than imposing an ad hoc dependence for the gravitational coupling, as previously done in the literature, in our proposal, the running of G emerges naturally from the internal dynamical structure of the theory. We explore the features of the resulting gravitational field for static and spherically symmetric mass distributions as well as within the cosmological framework.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2

References

  1. 1.

    M. Clifford, The confrontation between general relativity and experiment. Living Rev. Rel. 17, 4 (2014). arXiv:1403.7377 [gr-qc]

    Article  Google Scholar 

  2. 2.

    M. Armano, H. Audley, G. Auger, J.T. Baird et al., Sub-femto-\(g\) free fall for space-based gravitational wave observatories: lisa pathfinder results. Phys. Rev. Lett. 116, 231101 (2016)

    ADS  Article  Google Scholar 

  3. 3.

    J.P. Schwarz, D.S. Robertson, T.M. Niebauer, J.E. Faller, A free-fall determination of the Newtonian constant of gravity. Science 282, 2230–2234 (1998)

    ADS  Article  Google Scholar 

  4. 4.

    St Schlamminger, E. Holzschuh, W. Kündig, F. Nolting, R.E. Pixley, J. Schurr, U. Straumann, Measurement of Newton’s gravitational constant. Phys. Rev. D 74, 082001 (2006)

    ADS  Article  Google Scholar 

  5. 5.

    H.V. Parks, J.E. Faller, Simple pendulum determination of the gravitational constant. Phys. Rev. Lett. 105, 110801 (2010)

    ADS  Article  Google Scholar 

  6. 6.

    A. Bertoldi, L. Cacciapuoti, M. de Angelis, R.E. Drullinger, G. Ferrari, G. Lamporesi, N. Poli, M. Prevedelli, F. Sorrentino, G.M. Tino, Atom Interferometry for Precision Tests of Gravity: Measurement of G and Test of Newtonian Law at Micrometric Distances, in The Eleventh Marcel Grossmann Meeting On Recent Developments in Theoretical and Experimental General Relativity. Gravitation and Relativistic Field Theories (2008), pp. 2519–2529

  7. 7.

    G. Rosi, Challenging the ‘BigG’ measurement with atoms and light. J. Phys. B At Mol Opt Phys 49, 202002 (2016)

    ADS  Article  Google Scholar 

  8. 8.

    K. Koyama, J. Sakstein, Astrophysical probes of the Vainshtein mechanism: stars and galaxies. Phys. Rev. D 91, 124066 (2015). arXiv:1502.06872 [astro-ph.CO]

    ADS  MathSciNet  Article  Google Scholar 

  9. 9.

    P. Brax, Screening mechanisms in modified gravity. Class. Quantum Gravity 30, 214005 (2013)

    ADS  MathSciNet  Article  Google Scholar 

  10. 10.

    J. Khoury, Chameleon field theories. Class. Quantum Gravity 30, 214004 (2013). arXiv:1306.4326 [astro-ph.CO]

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    E. Babichev, C. Deffayet, An introduction to the Vainshtein mechanism. Class. Quantum Gravity 30, 184001 (2013)

    ADS  MathSciNet  Article  Google Scholar 

  12. 12.

    K. Koyama, Cosmological tests of modified gravity. Rept. Prog. Phys. 79, 046902 (2016). arXiv:1504.04623 [astro-ph.CO]

    ADS  Article  Google Scholar 

  13. 13.

    M. Ishak, Testing general relativity in cosmology. Living Rev. Rel. 22, 1 (2019). arXiv:1806.10122 [astro-ph.CO]

    Article  Google Scholar 

  14. 14.

    J.G. Williams, S.G. Turyshev, D.H. Boggs, Progress in lunar laser ranging tests of relativistic gravity. Phys. Rev. Lett. 93, 261101 (2004)

    ADS  Article  Google Scholar 

  15. 15.

    E.A. Milne, Relativity, Gravitation and World-Structure (The Clarendon Press, Oxford, 1935)

    Google Scholar 

  16. 16.

    P.A.M. Dirac, The cosmological constants. Nature 139, 323 (1937)

    ADS  Article  Google Scholar 

  17. 17.

    P.A.M. Dirac, New basis for cosmology. Proc. R. Soc. Lond. A A165, 199–208 (1938)

    ADS  Article  Google Scholar 

  18. 18.

    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972)

    Google Scholar 

  19. 19.

    J.-P. Uzan, Varying constants, gravitation and cosmology. Living Rev. Rel. 14, 2 (2011). arXiv:1009.5514 [astro-ph.CO]

    Article  Google Scholar 

  20. 20.

    P.S. Wesson, The implications for geophysics of modern cosmologies in which G is variable. Q. J. R. Astron. Soc. 14, 9 (1973)

    ADS  Google Scholar 

  21. 21.

    M.C. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 1993)

    Google Scholar 

  22. 22.

    L.F. Pavsteka, A.  Borschevsky, V.V. Flambaum, P.  Schwerdtfeger, Search for the variation of fundamental constants: strong enhancements in X\(\Pi \)2 cations of dihalogens and hydrogen halides. Phys. Rev. A 92, 012103 (2015). arXiv:1502.04451 [physics.chem-ph]

  23. 23.

    A.M.M. Pinho, C.J.A.P. Martins, Updated constraints on spatial variations of the fine-structure constant. Phys. Lett. B 756, 121–125 (2016). arXiv:1603.04498 [astro-ph.CO]

    ADS  Article  Google Scholar 

  24. 24.

    N.S. Oreshkina, S.M. Cavaletto, N. Michel, Z. Harman, C.H. Keitel, Hyperfine splitting in simple ions for the search of the variation of fundamental constants. Phys. Rev. A 96, 030501 (2017). arXiv:1703.09943 [physics.atom-ph]

  25. 25.

    C. Negrelli, L. Kraiselburd, S.J. Landau, E. García-Berro, Spatial variation of fundamental constants: testing models with thermonuclear supernovae. Int. J. Mod. Phys. D 27, 1850099 (2018). arXiv:1804.01521 [astro-ph.CO]

  26. 26.

    M.S. Safronova, The search for variation of fundamental constants with clocks. Ann. Phys. 531, 1800364 (2019)

    Article  Google Scholar 

  27. 27.

    C.J.A.P. Martins, M.P. Colomer, Fine-structure constant constraints on late-time dark energy transitions. Phys. Lett. B 791, 230–235 (2019). arXiv:1903.04310 [astro-ph.CO]

  28. 28.

    L. Giani, E. Frion, Testing the equivalence principle with strong lensing time delay variations (2020). arXiv:2005.07533 [astro-ph.CO]

  29. 29.

    P.T. Landsberg, N.T. Bishop, A principle of impotence allowing for Newtonian cosmologies with a time-dependent gravitational constant. Mon. Not. R. Astrn. Soc. 171, 279–286 (1975)

    ADS  Article  Google Scholar 

  30. 30.

    G.C. McVittie, Newtonian cosmology with a time-varying constant of gravitation. Mon. Not. R. Astron. Soc. 183, 749–764 (1978)

    ADS  Article  Google Scholar 

  31. 31.

    C. Duval, G.W. Gibbons, P. Horvathy, Celestial mechanics, conformal structures and gravitational waves. Phys. Rev. D 43, 3907–3922 (1991). arXiv:hep-th/0512188

  32. 32.

    D.M. Christodoulou, D. Kazanas, Interposing a varying gravitational constant between modified Newtonian dynamics and weak Weyl gravity. Mon. Not. R. Astron. Soc. Lett. 479, L143–L147 (2018)

    ADS  Article  Google Scholar 

  33. 33.

    J.D. Barrow, Time-varying G. Mon. Not. R. Astron. Soc. 282, 1397–1406 (1996)

    ADS  Article  Google Scholar 

  34. 34.

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

    ADS  MathSciNet  Article  Google Scholar 

  35. 35.

    E.A. Milne, A Newtonian expanding universe. Q. J. Math os–5, 64–72 (1934)

    ADS  Article  Google Scholar 

  36. 36.

    W.H. McCrea, E.A. Milne, Newtonian universes and the curvature of space. Q. J. Math. os–5, 73–80 (1934)

    ADS  Article  Google Scholar 

  37. 37.

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

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

We dedicate this work to the memory of Antonio Brasil Batista, one the founders of the research group Cosmo-ufes, who has introduced us to the problem of the variation of the gravitational coupling in newtonian and relativistic theories. We thank Davi C. Rodrigues for enlightening discussions on the subject of this paper. JCF thanks CNPq and FAPES for partial financial support. HV thanks CNPq and PROPP/UFOP for partial financial support. JDT thanks FAPES and CAPES for their support through the Profix program. TG thanks FAPES for their support.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hermano Velten.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fabris, J.C., Gomes, T., Toniato, J.D. et al. Newtonian-like gravity with variable G. Eur. Phys. J. Plus 136, 143 (2021). https://doi.org/10.1140/epjp/s13360-021-01146-z

Download citation