Abstract
After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.
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References
Adler, R., Bazin, R., Schiifer, M.: Introduction to General Relativity. McGraw-Hill, New York (1967)
Bondi, H.: Negative mass in general relativity. Rev. Mod. Phys. 29(3), 423 (1957)
Bonnor, W.B.: Negative mass and general relativity. Gen. Relativ. Gravit. 21(11), 1143–1157 (1989)
Combes, F.: Explaining the formation of bulges with MOND (2015a). arXiv:1501.03603v1
Combes, F.: Let’s dare to modify Newton’s law. Sci. Avenir 816, 34–35 (2015b)
El-Ad, H., Piran, T., da Costa, L.N.: Astrophys. J. Lett. 462, L13 (1996)
El-Ad, H., Piran, T., da Costa, L.N.: Mon. Not. R. Astron. Soc. 287(790), 429 (1997)
El-Ad, H., Piran, T.: Astrophys. J. 491, 421 (1997)
Faraoni, V.: The Lagrangian description of perfect fluids and modified gravity with extra force (2009). arXiv:0912.1249
Faraoni, V., Dent, J.B., Saridakis, E.N.: Covariantizing the interaction between dark energy and dark matter (2014). arXiv:1405.7288v2
Filippenko, A.V., Riess, A.G.: In: AIP Conf. Proc., vol. 540, pp. 227–246 (2001)
Hossenfelder, S.: A bimetric theory with exchange symmetry. Phys. Rev. D 78, 044015 (2008)
Henry-Couannier, F.: Int. J. Mod. Phys. A 20, 2341 (2005)
Knop, R., et al.: Astrophys. J. 598, 102 (2003)
Leibundgut, B.: Annu. Rev. Astron. Astrophys. 39, 67 (2001)
Milgrom, M.: Astrophys. J. 270, 365 (1983)
Milgrom, M.: Astrophys. J. 496, L89 (1998)
Milgrom, M., Sanders, R.H.: Astrophys. J. 658, 17 (2007)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Petit, J.P.: The missing mass problem. Nuovo Cimento B 109, 697–710 (1994)
Petit, J.P.: Twin Universe cosmology. Astrophys. Space Sci. 226, 273–307 (1995)
Petit, J.P., Midy, P., Landhseat, F.: Twin matter against dark matter. In: Conf. on Astr. and Cosm. “Where Is the Matter?”, Marseille (2001)
Petit, J.P., D’Agostini, G.: Negative mass in cosmology and nature of dark energy. Astrophys. Space Sci. 354, 611–615 (2014a)
Petit, J.P., D’Agostini, G.: Cosmological bimetric model with interacting positive and negative masses and two different speeds of light, in agreement with the observed acceleration of the universe. Mod. Phys. Lett. A 29(35c) (2014b). doi:10.1142/S021773231450182X
Petit, J.P., D’Agostini, G.: Cancellation of the central singularity of the Schwarzschild solution with natural mass inversion process. Mod. Phys. Lett. A (2015, accepted)
Petit, J.P., Lafont, X., Borallo, N.: 2D simulations of VLS with opposite masses populations. Unpublished (2015)
Piran, T.: On gravitational repulsion. Gen. Relativ. Gravit. 29(11), 1363 (1997)
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Riess, A.G.: Publ. Astron. Soc. Pac. 112, 1284 (2000)
Riess, A.G.: Astron. J. 607, 665–687 (2004)
Schwarzschild, K.: Über das Gravitational eines Massenpunktes nach der Einsteineschen Theory, pp. 189–196. Sitzber. Preuss. Akad. Wiss., Berlin (1916)
Souriau, J.M.: Structure des Systèmes Dynamiques Dunod, France (1970) (Structure of Dynamical Systems, Birkhaüser, Boston, 1997)
Tonry, J.T., et al.: Astrophys. J. 594, 1 (2003)
Weinberg, S.: The Quantum Theory of Fields. Cambridge University Press, Cambridge (2005)
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Petit, JP., D’Agostini, G. Lagrangian derivation of the two coupled field equations in the Janus cosmological model. Astrophys Space Sci 357, 67 (2015). https://doi.org/10.1007/s10509-015-2250-6
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DOI: https://doi.org/10.1007/s10509-015-2250-6