Tail effects of self-interacting scalar fields

We consider the effects of quartic self-interactions on the dynamics of a binary system due to a (nearly) massless scalar field conformally coupled to matter. We investigate the deviations from general relativity at the conservative level and put a bound on the self-coupling lambda less than or similar to (/32GNM2 circle dot)-1 where /3 is the conformal coupling of the scalar to matter. We also consider the radiative sector where we use the Schwinger-Keldysh formalism to find the tail interactions which couple the multipoles of the binary system and induce a small advance of the periastron.