Recent Progress in Gravitational Physics (2015–2025)

Measurements of the Gravitational Constant $G$

The Newtonian gravitational constant $G$ remains the least precisely known fundamental constant in physics. Over the past decade, multiple high-precision experiments (using torsion pendulums, torsion balances, beam balances, and atom interferometers) have yielded $G$ values that scatter by about 0.05% (500 ppm) – far exceeding their reported uncertainties 12. This is illustrated in Figure 1, which compares recent $G$ determinations by method. Each experiment reports $G \approx 6.673$–$6.675\times10^{-11}$ m³/kg·s² with relative uncertainties on the order of $10^{-5}$ to $10^{-4}$ (tens of ppm), yet the results do not statistically agree 32.

Figure 1: Recent precision measurements of the gravitational constant $G$. Points show the reported $G$ values (horizontal axis) from various experiments since the 1980s, grouped by measurement method. The error bars are the $1σ$ uncertainties. Colors/symbols indicate different experimental techniques (ToS: torsion pendulum time-of-swing; AAF: angular-acceleration feedback; compensation methods; free deflection; Fabry–Perot cavity; beam balance; cold-atom interferometry). The spread of results (roughly 50–500 ppm) far exceeds individual error bars, highlighting the inconsistency among measurements.)

Record-precision experiments: In 2018, researchers in China performed two simultaneous measurements using torsion pendulums: one using the time-of-swing (period shift) method and another using an angular-acceleration feedback method 3. They obtained:

  • $G = 6.674184(11)\times10^{-11}$ m³/kg·s²
  • $G = 6.674484(11)\times10^{-11}$ m³/kg·s²

(uncertainty ~12 ppm). These results differ from each other by about $4\times10^{-5}$ (40 ppm), which is several times the stated uncertainty. Likewise, a 2014 cold-atom interferometry experiment found $G = 6.67191(99)\times10^{-11}$ m³/kg·s² (150 ppm uncertainty) 4, noticeably lower than most torsion balance results.

Systematics vs. new physics: The prevailing view is that unknown systematic errors are the cause of the discrepancies, rather than real spatiotemporal $G$ variations 2. Experimenters have uncovered subtle systematics in past setups – for example, anelastic torsion fiber damping can bias the time-of-swing method by 100–300 ppm if uncorrected. A 2015 claim that $G$ measurements fluctuate periodically (correlated with Earth’s 5.9-year length-of-day cycle) 5 was largely dismissed after timing corrections weakened the supposed correlation. CODATA’s recommended $G$ now reflects a conservative uncertainty (~$2\times10^{-4}$%) to account for this dispersion 6.

Gravity on Intergalactic Scales (Galaxy & Cosmic Tests)

Galaxy rotation curves and MOND

Spiral galaxies exhibit flat rotation curves – star orbital speeds remain high at large radii, inconsistent with Newtonian decline. In GR, this implies massive dark matter halos. Modified Newtonian Dynamics (MOND) posits that below $a_0 \sim 1\times10^{-10}$ m/s², gravity deviates from Newton’s law.

Recent surveys (e.g., SPARC) confirm a tight correlation between observed centripetal acceleration $g_{\rm obs}=v^2/r$ and that predicted from baryonic matter $g_{\rm bar}$ 7. The Radial Acceleration Relation (RAR):

\[g_{\rm obs} \approx \sqrt{a_0\,g_{\rm bar}}, \quad (g \ll a_0)\]

is empirically very tight and universal across galaxies. MOND reproduces this naturally, but it struggles to explain mass in galaxy clusters without additional matter. The Bullet Cluster provides a strong case for collisionless dark matter – gravitational lensing centers do not coincide with the X-ray luminous gas 8.

Gravitational lensing and relativistic tests

Strong lensing studies (e.g. by Collett et al. 2018 on galaxy ESO 325–G004) measured the post-Newtonian parameter $\gamma = 0.97 \pm 0.09$ 9, consistent with GR ($\gamma = 1$). Weak lensing surveys (KiDS, DES) also show that gravitational lensing and galaxy dynamics follow GR’s predictions when dark matter is included. Any effective variation in $G$ on Mpc scales must be <1%.

Cosmological scale gravity

The Planck 2018 results show $\Lambda$CDM fits CMB data well with constant $G$ and GR. The GW170817 event established that $ v_{\rm gw} - c / c < 10^{-15}$, ruling out wide classes of modified gravity models with anomalous GW speed 10.

Emergent gravity (e.g., Verlinde 2016) offers a framework where gravity is an entropic force. It makes testable predictions, such as galaxy lensing profiles without dark matter. One study found consistency with KiDS data 11, though emergent gravity lacks a full cosmological description and struggles on cluster scales.

Gravitational-Wave Observatories and Local Gravity Stability

Gravitational wave detections (LIGO, Virgo, KAGRA) allow precise tests of strong-field and radiative gravity.

Tests of GR

Binary black hole mergers (e.g. GW150914) match GR waveforms to within 10% in phase evolution 12. LIGO/Virgo has not detected:

  • Any deviations in waveform phase
  • Non-GR polarization modes
  • Echoes or other exotic merger remnants

All observed GWs are consistent with GR predictions 12.

Propagation tests and $G$ variation

GW170817 showed GWs and gamma-rays arrived within 1.74 s after 130 million years’ travel, implying $v_{\rm gw} \approx c$ to $<10^{-15}$ 10. This rules out dispersive propagation due to a graviton mass or modified dispersion.

Gravitational waveform analysis also constrains time-varying $G$. The neutron star merger GW170817 sets limits on $ \Delta G/G \lesssim$ few % over 130 Myr 13. Future events will probe even tighter limits. Pulsar timing already restricts $\dot{G}/G \lesssim 10^{-12}$–$10^{-13}$ yr⁻¹.

Graviton mass

Waveform dispersion analyses yield graviton mass limits: $m_g \le 1.76\times10^{-23}$ eV/$c^2$, implying a range $\lambda_g \gtrsim 10^{16}$ km 14. Thus, gravity appears to have no short-range cutoff on galactic or cosmic scales.

Conclusion

  • $G$ remains difficult to measure precisely; variations across experiments are likely due to systematics, not new physics.
  • GR holds at galactic and cosmological scales, when dark matter and dark energy are included. Modified gravity models like MOND can fit galaxy data but struggle at cluster and cosmological levels.
  • Gravitational-wave data confirm GR’s predictions for waveform shape, speed, and polarization. They also severely constrain time variation of $G$ and graviton mass.
  • Overall, Einstein’s General Relativity, with a constant $G$, remains consistent with all experimental data from laboratory to cosmic scales.

References

  1. Quinn, T., Speake, C., Parks, H., & Davis, R. (2013). The Newtonian constant of gravitation: recent measurements and related studies. Philos. Trans. R. Soc. A, 372, 20140032. ↩

  2. Schlamminger, S., Gundlach, J.H., & Newman, R.D. (2015). Recent measurements of the gravitational constant as a function of time. Phys. Rev. D, 91, 121101(R). ↩ ↩2 ↩3

  3. Li, Q., et al. (2018). Measurements of the gravitational constant using two independent methods. Nature, 560, 582–588. ↩ ↩2

  4. Rosi, G., et al. (2014). Precision measurement of the Newtonian gravitational constant using cold atoms. Nature, 510, 518–521. ↩

  5. Anderson, J.D., et al. (2015). Measurements of Newton’s gravitational constant and the length of day. EPL, 110, 1002. ↩

  6. CODATA 2018 recommended values of the fundamental physical constants. ↩

  7. McGaugh, S., Lelli, F., & Schombert, J. (2016). The Radial Acceleration Relation in Rotationally Supported Galaxies. Phys. Rev. Lett., 117, 201101. ↩

  8. Clowe, D., et al. (2006). A Direct Empirical Proof of the Existence of Dark Matter. ApJ, 648, L109–L113. ↩

  9. Collett, T.E., et al. (2018). A precise extragalactic test of General Relativity. Science, 360, 1342–1346. ↩

  10. Abbott, B.P., et al. (2017). GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett., 119, 161101. ↩ ↩2

  11. Brouwer, M.M., et al. (2017). First test of Verlinde’s theory of Emergent Gravity using weak gravitational lensing. MNRAS, 466, 2547–2559. ↩

  12. Abbott, B.P., et al. (2016–2021). Tests of general relativity with GWTC-1 and GWTC-2 events. Phys. Rev. Lett., ApJL, CQG. ↩ ↩2

  13. Desai, S. (2018). Limit on the time variation of Newton’s constant using GW170817. Mod. Phys. Lett. A, 33, 1850224. ↩

  14. Abbott, B.P., et al. (2016). Tests of gravitational-wave propagation and polarization in the LIGO–Virgo observations. Phys. Rev. Lett., 116, 221101. ↩