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A new, field-theory-based framework for discussing and interpreting tests ofgravity, notably at the second post-Newtonian (2PN) level, is introduced.Contrary to previous frameworks which attempted at parametrizing anyconceivable deviation from general relativity, we focus on the best motivatedclass of models, in which gravity is mediated by a tensor field together withone or several scalar fields. The 2PN approximation of these"tensor-multi-scalar" theories is obtained thanks to a diagrammatic expansionwhich allows us to compute the Lagrangian describing the motion of N bodies. Incontrast with previous studies which had to introduce many phenomenologicalparameters, we find that the 2PN deviations from general relativity can befully described by only two new 2PN parameters, epsilon and zeta, beyond theusual (Eddington) 1PN parameters beta and gamma. It follows from the basictenets of field theory, notably the absence of negative-energy excitations,that (beta-1), epsilon and zeta (as well as any new parameter entering higherpost-Newtonian orders) must tend to zero with (gamma-1). It is also found thatepsilon and zeta do not enter the 2PN equations of motion of light. Therefore,light-deflection or time-delay experiments cannot probe any theoreticallymotivated 2PN deviation from general relativity, but they can give a cleanaccess to (gamma-1), which is of greatest significance as it measures the basiccoupling strength of matter to the scalar fields. Because of the importance ofself-gravity effects in neutron stars, binary-pulsar experiments are found toconstitute a unique testing ground for the 2PN structure of gravity. Asimplified analysis of four binary pulsars already leads to significantconstraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.Comment: 63 pages, 11 figures.ps.tar.gz.uu, REVTeX 3.

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