Tidal effects up to next-to-next-to-leading post-Newtonian order in massless scalar-tensor theories

Abstract

In this paper, we study the tidal effects in the gravitationally bound two-body system at next-to-next-to leading post-Newtonian order for spinless sources in massless scalar-tensor theories. We compute the conservative dynamics, using both a Fokker Lagrangian approach and effective field theory with the post-Newtonian effective field theory formalism. We also compute the ten conserved quantities at the same next-to-next-to leading order. Finally, we extend our results from simple scalar-tensor theories to Einstein-scalar-Gauss-Bonnet gravity. Such results are important in preparation of the science case of the next generation of gravitational wave detectors.