Solar-system experimental constraints on nonlocal gravity

TL;DR

This work constrains Deser-Woodard nonlocal gravity in a static, spherically symmetric Solar-System background by deriving geodesic motion and computing four observables—light deflection, Shapiro time delay, perihelion precession, and geodetic precession—and comparing them with VLBI, Cassini, MESSENGER, and GP-B/LLR data. The analysis shows that increasing the decay parameter $b$ weakens the bounds on the nonlocal strength $\\zeta$, with perihelion precession near $b\\approx 1.06$ delivering the tightest single-limit, $|\\zeta|\\lesssim 3\\times 10^{-10}$. By combining all four experiments, the authors map a well-defined, sharply bounded allowed region in the $(\\zeta,b)$ plane, highlighting the complementarity of different Solar-System tests. The results affirm no detectable deviation from General Relativity within the studied parameter range and provide precise targets for future extensions to rotating backgrounds and higher-precision missions.

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 $(ζ,b)$.

Figures (2)

• Figure 1: The angle of perihelion advance varying with $b$ for $\zeta=0.0001$ Perihelion advance $\Delta\phi$ as a function of the parameter $b$ for the Schwarzschild limit ($\zeta=0$) and for a nonlocal gravity deformation ($\zeta = 0.0001$). The deformation significantly enhances the perihelion advance when $b$ is close to unity, producing a sharp peak around $b\simeq 1.06$, while for $b\gtrsim 1.2$ the effect becomes negligible and the two curves almost converges.
• Figure 2: The total constraint of the parameters $(\zeta,b)$ obtained from the four tests considered in this work. The bounds derived from the light deflection(LD), Shapiro time delay(STD), perihelion advance(PA) and geodetic precession(GP) are show by the red, green, orange and bule dashed line, respectively. The shaded gray region indicates the parameter space bounded by all experiments.