Model‐independent constraints on r^‐3 extra‐interactions from orbital motions

Abstract

Constraints on long-range power-law modifications Upert ∝ r −3 of the usual Newtonian gravitational potential UN ∝ r −1 are inferred from orbital motions of well known artificial and natural bodies. They can be interpreted in terms of a characteristic length ℓ which may be identified with, e.g., the anti-de Sitter (AdS) radius of curvature ℓ in the Randall-Sundrum (RS) braneworld model, although this not a mandatory choice. Our bounds, complementary to those from tabletop laboratory experiments, do not rely upon more or less speculative and untested theoretical assumptions, contrary to other long-range RS tests proposed in astrophysical scenarios in which many of the phenomena adopted may depend on the system's composition, formation and dynamical history as well. Independently of the interpretation of ℓ, the perihelion precession of Mercury and its radiotechnical ranging from the Earth yield ℓ 10 − 50 km. Tighter bounds come from the perigee precession of the Moon, from which it can be inferred ℓ 500 − 700 m. The best constraints (ℓ 5 m) come from the Satellite-to-Satellite Tracking (SST) range of the GRACE A/B spacecrafts orbiting the Earth: proposed follow-on of such a mission, implying a sub-nm s −1 range-rate accuracy, may constrain ℓ at ∼ 10 cm level. Weaker constraints come from the double pulsar system (ℓ 80 − 100 km) and from the main sequence star S2 orbiting the compact object in Sgr A * (ℓ 6.2 − 8.8 AU). Such bounds on the length ℓ, which must not necessarily be identified with the AdS radius of curvature of the RS model, naturally translate into constraints on an, e.g., universal coupling parameter K of the r −3 interaction. GRACE yields K ≤ 1 × 10 16 m 5 s −2 .

Constraints on extra dimensions from precision molecular spectroscopy

“…The micrometer-to-millimeter range is probed in torsion-balance type experiments, with the tightest constraint obtained by Kapner et al [46] for a single extra dimension of < × − R 4.4 10 1 5 m. The centimeter-to-meter separations are accessed by Cavendish-or Eötvöstype investigations in the laboratory, while astronomical scales can be probed in satellite or planetary orbits that also serve to constrain the universality of free fall and deviations from the gravitational inverse-square law [40]. Constraints for the RS-theories are obtained by Iorio [47] using data from the orbital motions of satellites or astronomical objects, with the tightest constraint for the inverse of the curvature of < k 1 5 m obtained from the motion of the GRACE satellite. The latter constraint is in the ≫ kr 1 regime of equation (14) and probes a different distance range to that of molecules ( ≪ kr 1).…”

Probing extra dimension through gravitational wave observations of compact binaries and their electromagnetic counterparts

“…Therefore, in high-dimensional braneworld models, the hypothesis of small extra dimensions is a common way to restore four-dimensional Newtonian 9 gravitational potential. According to current experiments within the solar system [66][67][68][69], Newtonian gravity is applicable in the sub-millimeter range, which means that the radius of the extra dimension should be less than 0.1 mm. In our braneworld model, this requires that the AdS radius l, which stands for the scale of the extra dimension, is small (l < 0.1 mm).…”

Local cosmological effects of the order of H in the orbital motion of a binary system

“…where K may or may not depend on GM along with other parameter(s) {α}. It can be shown perturbatively that the resulting orbital precessions are Iorio 2012b) (Hořava 2009b,a) predicts the existence of an additional radial acceleration…”