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

Abstract: In this article, we study the tidal effects in the gravitationally bound two-body system at next-to-next-to leading post-Newtonian order for spin-less sources in massless scalar-tensor theories. We compute the conservative dynamics, using both a Fokker Lagrangian approach and effective field theory with the PN-EFT formalism. We also compute the ten conserved quantities at the same NNLO order. Finally, we extend our results from simple ST 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.