Solar-system experimental constraints on nonlocal gravity

TL;DR

This paper constrains the parameters of a nonlocal gravity model using high-precision Solar-System experiments, finding tight bounds on the model's parameters and identifying the most sensitive observational tests.

Contribution

It provides the first comprehensive analysis of Solar-System constraints on the Deser-Woodard nonlocal gravity model, combining multiple experiments to tightly bound its parameters.

Findings

Larger $b$ weakens nonlocal effects, relaxing constraints on $ig

Perihelion advance is most sensitive to $ig$ near $ba0b1a0 1.06

Combined experiments define a sharply bounded parameter space for $(ig,b)$

Abstract

In this work, we study the constraints on the characteristic parameters $(\zeta,b)$ 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 $\zeta$. The perihelion advance exhibits the strongest sensitivity to $\zeta$ 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 $(\zeta,b)$.