Solar-system experimental constraints on nonlocal gravity

Abstract: In this work, we study the constraints on the characteristic parameters $(ζ,b)$ of the Deser-Woodard nonlocal gravity model in a static and spherically symmetric background, using four classes of high-precision Solar-System experiments: stellar light deflection, Shapiro time delay, perihelion advance, and geodetic precession. From geodesic equations, we derive observable geometric quantities that can be directly compared with VLBI/VLBA astrometry, the Cassini time-delay measurement, MESSENGER data and the GP-B/LLR results. Our results show that a larger value of $b$ suppresses the nonlocal effect more rapidly with radius, thereby weakening the overall constraints on $ζ$. The perihelion advance exhibits the strongest sensitivity to $ζ$ around $b\simeq 1.06$, providing the tightest single experiment bound, whereas away from this region the combined constraint becomes dominated by the Shapiro time delay. Incorporating all four experiments yields a well-defined and sharply bounded allowed region for the parameter space $(ζ,b)$.