Testing gravity to second post-Newtonian order: A field-theory approach.

A new, field-theory-based framework for discussing and interpreting experimental tests of relativistic gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable phenomenological deviation from general relativity, we focus on the most general class of gravity models of the type suggested by unified theories: namely models in which gravity is mediated by a tensor field together with one or several scalar fields. The 2PN approximation of these “tensor–multi-scalar” theories is obtained thanks to a diagrammatic expansion which allows us to compute the Lagrangian describing the motion of N bodies. In contrast with previous studies which had to introduce many phenomenological parameters, we find that the 2PN deviations from general relativity can be fully described by introducing only two new 2PN parameters, " and �, beyond the usual (Eddington) 1PN parameters � ≡ � − 1 and ≡ − 1. It follows from the basic tenets of field theory (notably the absence of negative-energy excitations), that �, " and � (as well as all the further parameters entering higher post-Newtonian orders) must tend