Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity

We study the conservative dynamics of spinless compact objects in a general effective theory of gravity which includes a metric and an arbitrary number of scalar fields, through $\mathcal{O}(G^{3})$. Departures from Einstein gravity, which preserve general coordinate and local Lorentz invariance, are characterized by higher-derivative terms in a Lagrangian whose coupling constants scale as powers of a ``new-physics'' length scale, $\ell$. For a purely metric theory we compute the contributions from the the leading and subleading higher-curvature curvature corrections. In four dimensions these are cubic and quartic curvature terms, i.e. orders $\ell^4$ and $\ell^6$. We also study a general multi-scalar-tensor theory of gravity to order $\ell^{4}$, which includes both Einstein-dilaton-Gauss-Bonnet (EdGB) and dynamical Chern-Simons (dCS) higher-order couplings. Specifically, we compute the radial action in a post-Minkowskian approximation for scattering orbits, to two-loop order. The result encodes the fully relativistic dynamics of the compact objects, and serves as a generating function for gauge-invariant orbital observables for both bound and unbound binary systems. Where overlapping post-Newtonian results are available, we've verified agreement.