Post-Newtonian parameters from alternative theories of gravity
Theories of gravity representing alternatives of the Theory of General relativity (GRT) have been studied for different reasons since the foundation of GRT. To test the theoretical consistence of these theories with observational data it is necessary to examine and to fit the standard tests for GRT, in particular, solar system observations and tests on galactic scales. To this end, it is inevitable to go beyond the PPN formalism developed for metric theories to test them on the solar system scale. In this paper, for a special class of theories, the authors provide a general framework (in the Palatini formalism) to test theories at the solar system level and possibly at the galactic level (the latter point is announced to be considered in a forthcoming paper). The authors focus their analysis on those theories of gravity, for which the purely geometric part of the Lagrangian is given by any real analytic function \(L(R)\) of the Ricci scalar \(R\), where \(R\) is formed from a metric and a torsionless connection given independently of the metric. After discussing the corresponding field equations and some vacuum solution, for a subclass of these Lagrangians containing the Ricci scalar as an item, the linear approximation of the field equation is written and discussed for the cases that a flat and an (anti-) de-Sitter space-time background are perturbed. It is shown that both in the vacuum and the matter case the deviation from GRT 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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