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

Abstract

A new, field-theory-based framework for discussing and interpreting tests of gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable deviation from general relativity, we focus on the best motivated class of 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 only two new 2PN parameters, epsilon and zeta, beyond the usual (Eddington) 1PN parameters beta and gamma. It follows from the basic tenets of field theory, notably the absence of negative-energy excitations, that (beta-1), epsilon and zeta (as well as any new parameter entering higher post-Newtonian orders) must tend to zero with (gamma-1). It is also found that epsilon and zeta do not enter the 2PN equations of motion of light. Therefore, light-deflection or time-delay experiments cannot probe any theoretically motivated 2PN deviation from general relativity, but they can give a clean access to (gamma-1), which is of greatest significance as it measures the basic coupling strength of matter to the scalar fields. Because of the importance of self-gravity effects in neutron stars, binary-pulsar experiments are found to constitute a unique testing ground for the 2PN structure of gravity. A simplified analysis of four binary pulsars already leads to significant constraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.