Abstract
In light of the recent interest in dynamical dark energy models based on a cosmology with varying gravitational and cosmological parameters \(G\) and \(\varLambda\), we present here a model of inertia in a type of Friedmann universe with \(G = G_{0}(A/A_{0})^{\sigma}\); \(A\) being the dimensionless scale factor, that was recently studied by Singh et al. (Astrophys. Space Sci. 345:213, 2013). The proposed Machian model of inertia utilizes the curved space generalization of Sciama’s law of inertial induction, which is based on the analogy between the retarded far fields of electrodynamics and those of gravitation, and expresses the total inertial force \(F= -ma\) on an accelerating mass \(m\) in terms of contributions from all matter in the observable Universe. We show that for a varying Friedmann model with \(\sigma=-3/2\), inertial induction alone can account for the total inertial force on the accelerating mass. We then compare this cosmological model with current observational constraints for the variation of \(G\).
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References
Abbussattar, Vishwakarma, R.G.: Class. Quantum Gravity 14, 945 (1997)
Abdel-Rahaman, A.-M.M.: Gen. Relativ. Gravit. 22, 665 (1990)
Accetta, F.C., Krauss, K.M., Romanelli, P.L.: Phys. Lett. B 278, 146 (1990)
Arbab, A.I.: Gen. Relativ. Gravit. 29, 61 (1997)
Arzoumanian, Z.: PhD thesis, Princeton University Press, 1995
Bañados, M., Silk, J., West, S.W.: Phys. Rev. Lett. 103, 111102 (2009)
Barbour, J.B.: In: Barbour, J.B., Pfister (eds.) Mach’s Principle: From Newton’s Bucket to Quantum Gravity. Birkhauser, Basel (1995)
Barrow, J.D.: Phys. Rev. D 35, 1805 (1987)
Benvenuto, O.G., Garcia-Berro, E., Isern, J.: Phys. Rev. D 69, 082002 (2004)
Berman, M.S.: Gen. Relativ. Gravit. 23, 465 (1991a)
Berman, M.S.: Phys. Rev. D 43, 1075 (1991b)
Berman, M.S.: Astrophys. Space Sci. 318, 269 (2008)
Berman, M.S.: Int. J. Theor. Phys. 48, 3257 (2009)
Berry, M.V.: Principles of Cosmology and Gravitation. Cambridge University Press, Cambridge (1976)
Bertolami, O.: Nuovo Cimento B 93, 36 (1986)
Bottino, A., Kim, C.W., Song, J.: Phys. Lett. B 351, 116 (1995)
Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961)
Carroll, S.M.: Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley, Reading (2004)
Copi, C.J., Davis, A.N., Krauss, L.M.: Phys. Rev. Lett. 92, 171301 (2004)
Crawford, J.P., Kazanas, D.: Astrophys. J. 701, 1701 (2009)
Dirac, P.A.M.: Nature 139, 323 (1937)
Dirac, P.A.M.: Proc. R. Soc. Lond. A 365, 19 (1979)
Freese, K., et al.: Nucl. Phys. B 287, 797 (1987)
Gaztanaga, E., et al.: Phys. Rev. D 65, 023506 (2001)
Giné, J.: Int. J. Theor. Phys. 50, 607 (2011)
Goldman, T., et al.: Phys. Lett. B 281, 219 (1992)
Graneau, P., Graneau, N.: Gen. Relativ. Gravit. 35, 751 (2003)
Guenther, D.B., et al.: Astrophys. J. 498, 871 (1998)
Haisch, B., Rueda, A., Puthoff, H.E.: Phys. Rev. A 49, 678 (1994)
Hellings, R.W.: In: Melinkov, V. (ed.) Problems in Gravitation. State University Press, Moscow (1987)
Jamil, M., Debnath, U.: Int. J. Theor. Phys. 50, 1602 (2011)
Jordan, P.: Naturwissenschaften 26, 417 (1938)
Kalligas, D., Wesson, P., Everitt, C.W.F.: Gen. Relativ. Gravit. 24, 351 (1992)
Kaspi, V.M., Taylor, J.H., Ryba, M.: Astrophys. J. 428, 713 (1994)
Kazanas, D.: Astrophys. J. 241, L59 (1980)
Lau, Y.: Aust. J. Phys. 38, 547 (1985)
Lense, J., Thirring, H.: Phys. Z. 19, 156 (1918)
Li, Y.: Class. Quantum Gravity 28, 225006 (2011)
Mach, E.: The Science of Mechanics—A Critical Historical Account of Its Development. Open Court, La Salle (1960)
Martins, A.A., Pinheiro, M.J.: Int. J. Theor. Phys. 47, 2706 (2008)
McGaugh, S.S.: Can. J. Phys. 93, 250 (2015)
Moffat, J.W.: J. Cosmol. Astropart. Phys. 03, 004 (2006)
Moffat, J.W., Toth, J.W.: Mon. Not. R. Astron. Soc. 395, L25 (2009)
Nordtvedt, K.: Phys. Rev. 169, 1017 (1968)
Peebles, P.J.E., Ratra, B.: Astrophys. J. 325, L17 (1988)
Peters, P.C.: J. Math. Phys. 10, 1216 (1969)
Ponce de Leone, J.: Class. Quantum Gravity 20, 5321 (2003)
Ponce de Leon, J.: Class. Quantum Gravity 29, 135009 (2012)
Pradhan, A., Singh, A.K., Otarod, S.: Rom. J. Phys. 52, 445 (2007)
Ratra, B., Peebles, P.J.E.: Phys. Rev. D 37, 3406 (1988)
Ray, S., et al.: Int. J. Mod. Phys. D 16, 1791 (2007)
Ray, S., et al.: Int. J. Theor. Phys. 50, 2687 (2011)
Reasenberg, R.D.: Philos. Trans. R. Soc. A 310, 227 (1983)
Reuter, M., Weyer, H.: Phys. Rev. D 70, 124028 (2004)
Rindler, W., Ishak, M.: Phys. Rev. D 76, 043006 (2007)
Rubano, C., Scudellaro, P.: Gen. Relativ. Gravit. 37, 521 (2005)
Sciama, D.W.: Mon. Not. R. Astron. Soc. 113, 34 (1953)
Signore, R.: Nuovo Cimento 112B, 1593 (1997)
Singh, N.I., Devi, Y.B., Singh, S.S.: Astrophys. Space Sci. 345, 213 (2013)
Singh, T., Beesham, A., Mbokazi, W.S.: Gen. Relativ. Gravit. 30, 573 (1998)
Stairs, I.H.: Living Rev. Relativ. 6, 5 (2003)
Sistero, F.R.: Gen. Relativ. Gravit. 23, 1265 (1991)
Štefančić, H.: Phys. Lett. B 595, 9 (2004)
Sultana, J., Kazanas, D.: Int. J. Mod. Phys. D 20, 1205 (2011)
Sultana, J., Bose, B., Kazanas, D.: Int. J. Mod. Phys. D 23, 1450090 (2014)
Turyshev, S.G., et al.: In: Karshenboim, S.G. (ed.) Astrophysics, Clocks and Fundamental Constants. Lecture Notes in Physics, vol. 648. WE Heraeus Stift, Hanau (2004)
Uzan, J.P.: Living Rev. Relativ. 14, 2 (2011)
Williams, J.G., Sinclair, W.S., Yoder, C.F.: Geophys. Res. Lett. 5, 943 (1978)
Acknowledgements
J.S. gratefully acknowledges financial support from the University of Malta during his visit at NASA-GSFC and the hospitality of the Astrophysics Science Division of GSFC.
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Sultana, J., Kazanas, D. Inertia in Friedmann Universes with variable \(G\) and \(\varLambda\) . Astrophys Space Sci 359, 9 (2015). https://doi.org/10.1007/s10509-015-2452-y
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DOI: https://doi.org/10.1007/s10509-015-2452-y