Abstract
Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On the other hand, approximate solutions are found in matter cases starting from a Lagrangian which depends on a phenomenological parameter. Both in the vacuum case and in the matter case the deviations from General Relativity are controlled by parameters that provide the Post-Newtonian corrections which prove to be in good agreement with solar system experiments.
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Perlmutter, S., et al.: ApJ 517, 565 (1999) [astro-ph/9812133]; Perlmutter el al.: Nature 404, 955 (2000); Astroph, J.: 517, 565 (1999); Riess, A.G., et al.: AJ 116, 1009 (1999) [astro-ph/9805201]; Spergel, D.N., et al.: ApJS 148, 175 (2003); Verde, L., et al.: MNRAS 335, 432 (2002).
Dvali, G., Gabadadze, G., Porrati, M.: Phys. Lett. B 485, 208 (2000) [hep-th/0005016]; Dvali, G., Gruzinov, A., Zaldarriaga, M.: Phys. Rev. D 68, 24012 (2003); Freese, K., Lewis, M.: Phys. Lett. B 540, 1 (2002) [astro-ph/0201229]; Aref'eva, I.Ya., Joukovskaya, L.V.: [hep-th/0504200]; Aref'eva, I.Ya., Koshelev, A.S., Vernov, S.Yu.: [astro-ph/0412619]; Nojiri, S., Odintsov, S.D.: [hep-th/0307071]
Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: [astro-ph/0306438]; Capozziello, S., Carloni, S., Troisi, A.: Recent Research Developments in Astronomy and Astrophysics -RSP/AA/21-2003 [astro-ph/0303041]; Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002); Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Int. J. Mod. Phys. D 12, 1969 (2003)
Starobinsky, A.A.: Phys, Lett. B 91, 99 (1980)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003) [hep-th/0307288]; Gen. Rel. Grav. 36, 1765 (2004) [hep-th/0308176]; Mod. Phys. Lett. A 19, 627 (2004) [hep-th/0310045]; Olmo, G.J. [gr-qc/0505135]
Vollick, D.N.: Phys. Rev. D 68, 063510 (2003); Allemandi, G., Borowiec, A., Francaviglia,~M.: Phys. Rev. D 70, 043524 (2004) [hep-th/0403264]; Olmo, G.J.: [gr-qc/0505101]; Olmo, G.J., Komp, W.: [gr-qc/0403092]; Meng, X.H., Wang, P.: Class. Quant. Grav. 20, 4949–4962 (2003) [astro-ph/0307354]; Meng, X.H., Wang, P.: Class. Quant. Grav. 21, 951–960 (2004) [astro-ph/0308031]; Kremer, G.M., Alves, D.S.M.: [gr-qc/0404082]; Olmo, G.J.: [gr-qc/0505136]; Allemandi, G., Borowiec, A., Francaviglia, M., Odintsov, S.D.: [gr-qc/0504057]
Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: JCAP0502, 010 (2005) [hep-th/0501096]
Will, C.: Living Reviews in Relativity, lrr-2001-4 (http://www.livingreviews.org)
Chiba, T.: Phys. Lett. B 575, 1–3 (2003) [astro-ph/0307338]; Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1-4 (2003) [astro-ph/0307285]; Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003) [hep-th/0307288]; Capozziello, S.: [gr-qc/0412088]
Barraco, D., Hamity, V. H.: Gen. Rel. Grav. 25, 461–471; Barraco, D., Hamity, V.H.: Gen. Rel. Grav. 28, 339–345 (1996); Meng, X.H., Wang, P.: Class. Quant. Grav. 20 4949–4962 (2003) [astro-ph/0307354]; Class. Quant. Grav. 21 951–960 (2004) [astro-ph/0308031]; [astro-ph/0308284]; Vollick, D. N.: [gr-qc/0312041]
Barraco, D., Hamity, V.H., Vucetich, H.: Gen. Rel. Grav. 34(4), 533–547 (2002)
Dominguez, A.E., Barraco, D.E.: Phys. Rev. D 70, 043505 (2004) [gr-qc/0408069]
Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Phys. Lett. A 326, 292–296 (2004)
Allemandi, G., Ruggiero, M.L.: in preparation
Buchdahl, H.A.: J. Phys. A 12(8), 1229 (1979); Buchdahl, H.A.: Proc. Camb. Phil. Soc. 68, 396 (1960)
Ferraris, M., Francaviglia, M., Volovich, I.: Nouvo Cim. B 108, 1313 (1993) [gr-qc/9303007]; Ferraris, M., Francaviglia, M., Volovich, I.: Class. Quant. Grav. 11, 1505 (1994)
Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge University Press, Cambridge (1973)
Ohanian Hans, C., Ruffini, R.: Gravitation and Spacetime. W.W. Norton and Company, New York (1994)
Straumann, N.: General Relativity, Springer, Berlin (2004)
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Allemandi, G., Francaviglia, M., Ruggiero, M.L. et al. Post-newtonian parameters from alternative theories of gravity. Gen Relativ Gravit 37, 1891–1904 (2005). https://doi.org/10.1007/s10714-005-0195-8
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DOI: https://doi.org/10.1007/s10714-005-0195-8