Worldline EFT treatment of quadratic and cubic gravity theories

Abstract: This paper explores modifications to General Relativity (GR) by considering higher-order curvature terms in the gravitational action, specifically focusing on the quadratic Ricci scalar and a particular cubic contraction of the Riemann tensor. These modifications introduce new interactions at short distances, potentially altering the dynamics of compact objects. We calculate the effective two-body binding potential energy for these modified theories to quantify these effects using the worldline effective field theory (WEFT) formalism. This approach allows us to systematically integrate out short-distance gravitational effects, capturing the modifications to the binding potential. Our results demonstrate how the quadratic Ricci scalar and cubic Riemann tensor terms contribute to the two-body interaction at the leading order, highlighting deviations from classical GR predictions. These findings provide insight into the possible observational signatures of such modified gravity theories in binary systems and other astrophysical settings.