In this paper we study the observational constraints that can be imposed on the coupling parameter $\widehat{\alpha }$ of the regularized version of the four-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit and apply our results to observations of a wide array of physical systems that admit such a description. We find that the Laser Geometric Environmental Observation Survey satellites are the most constraining, requiring $|\widehat{\alpha }|\lesssim {10}^{10}{\mathrm{m}}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early Universe ($t<{10}^{-3}\mathrm{s}$) or the immediate vicinity of stellar-mass black holes ($M\lesssim 100M_{\odot }$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and tabletop experiments. It is found that early Universe inflation prohibits all but the smallest negative values of $\widehat{\alpha }$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0\lesssim \widehat{\alpha }\lesssim {10}^8{\mathrm{m}}^2$.

• Received 29 June 2020
• Accepted 10 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.084005