How to Uncover the Secrets of the Gravitational Wave Background?

By Atif SuhailReviewed by Louis CastelJun 10 2025

Gravitational waves are ripples in spacetime generated by accelerated masses, predicted by Einstein’s general relativity. While individual gravitational wave events, like binary black hole mergers, have already been detected, a more elusive target remains: the gravitational wave background (GWB). This is a superposition of countless unresolved sources of gravitational waves arriving from all directions. The GWB is expected to carry rich information about the early universe, including signals from inflation, cosmic strings, and massive black hole binaries.^1-2

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Since 2015, the LIGO and Virgo observatories have successfully detected high-frequency gravitational waves from cataclysmic astrophysical events such as black hole and neutron star mergers. These achievements have revolutionized astrophysics, confirming the existence of previously unseen objects and offering a new way to observe the universe.¹

However, ground-based detectors like LIGO and Virgo are limited by seismic and thermal noise, making them blind to ultra-low-frequency signals in the nanohertz range, precisely where the GWB is expected to be most prominent.

Pulsar Timing Arrays (PTAs), including NANOGrav, the European PTA, and the Parkes PTA, offer a solution by using the regular pulses from millisecond pulsars as cosmic clocks. Variations in pulse arrival times across multiple pulsars can reveal the presence of gravitational waves. However, PTA detection requires decades of ultra-precise timing data, and the method is sensitive primarily to the radial component of spacetime perturbations.^1-2

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Key Findings and Innovation

Jeremy Darling, an astrophysicist at the University of Colorado, has introduced a novel method to search for the low-frequency stochastic GWB using astrometry, specifically the apparent angular motion of quasars. Along with collaborators and building on earlier work, Darling used data from the Gaia space observatory, analyzing over a billion quasar pairs to detect correlated angular shifts that could indicate the presence of gravitational waves.³

• Using VLBI and Gaia for Angular Position Tracking:

Darling’s method leverages the technique of very long baseline interferometry (VLBI) and optical astrometry from Gaia to measure tiny angular deflections in the positions of distant quasars and galaxies over time. Instead of relying on time delays in pulsar signals, this approach detects spatial displacements caused by gravitational waves. These displacements are subtle, on the order of microarcseconds per year, and manifest as a global pattern in quasar motion.⁴

• Correlated Angular Motion as a Gravitational Wave Signature:

The method focuses on how gravitational waves cause transverse shifts (changes in the apparent angular positions of objects on the sky) as the wavefronts pass through space. Over time, a stochastic background of gravitational waves should imprint a specific angular correlation pattern (described by the astrometric Hellings–Downs curve) in the proper motions of extragalactic sources. Darling’s team analyzed Gaia DR3 data for over a million quasars and calculated proper motion correlations across more than 2 billion quasar pairs, successfully constructing the first astrometric Hellings–Downs curve.^3-4

• A Shift from Timing to Astrometry:

Unlike pulsar timing arrays (PTAs), which detect gravitational waves by measuring delays in radio pulse arrival times from pulsars, Darling’s method shifts focus to angular deflections. This angular approach opens a new observational window at ultra-low frequencies (frequencies even lower than those accessible by PTAs) allowing cross-checks of signals detected via timing and offering a pathway to explore new source classes such as exotic cosmological backgrounds or ultra-massive black hole binaries.⁴

This technique represents a major innovation in gravitational wave astronomy, demonstrating that spatial correlations in quasar motion can serve as a powerful, complementary probe of the gravitational wave background, one that may help disentangle the origins and nature of the stochastic signals seen in other channels.⁵

Methodology

Jeremy Darling and his team introduced an innovative observational approach to detect the low-frequency stochastic gravitational wave background by examining the apparent angular motion (proper motions) of distant quasars. Unlike pulsar timing arrays that rely on timing shifts, their method tracks spatial deflections using VLBI and high-precision optical astrometry from the Gaia DR3 Quaia catalog.^3-4

They analyzed over 1.1 million quasars covering 73% of the sky, focusing on sources with low proper motion amplitudes (<100 μas/yr) to reduce noise. By leveraging this extensive archival dataset, they were able to evaluate angular correlations across more than two billion quasar pairs, marking the largest-scale astrometric analysis ever conducted for gravitational wave detection.⁴

Statistical Methods: Two main mathematical frameworks were used to interpret the signal patterns:

• Vector Spherical Harmonics (VSH): The gravitational wave signal, if present, would appear dominantly in the quadrupole modes of the angular power spectrum. Darling applied least-squares fitting to extract both E-mode (spheroidal) and B-mode (toroidal) dipole and quadrupole components.
• Astrometric Hellings–Downs (HD) Curve: A generalized HD curve, adapted for angular motions (rather than timing residuals), was calculated by cross-correlating quasar pair proper motions as a function of angular separation. The goal was to detect a specific quadrupolar pattern consistent with a gravitational wave background. The null results in mixed-mode cross-correlations served as a built-in systematic error check. By binning quasar pairs by angular separation and calculating the error-weighted correlation of their proper motions (both parallel and perpendicular components), Darling's team tested for statistically significant patterns matching the HD curve.^{3, 6}

Darling's approach is not a competitor to existing PTA efforts like NANOGrav but complements them. While PTAs are highly sensitive to gravitational waves in the 1–100 nanohertz range through time-of-arrival residuals of pulsar signals, astrometric techniques probe transverse angular deflections (another physical manifestation of gravitational waves) across similar and even lower frequencies.³

Moreover, PTAs measure radial effects, while Darling’s method probes angular motions, adding a new dimension to gravitational wave studies. The potential to cross-correlate both methods in the future could enhance the sensitivity and robustness of gravitational wave background detections, helping to constrain sources such as massive black hole binaries or cosmological phenomena.^3-4

Implications

Darling’s technique opens a new observational window: gravitational waves with frequencies as low as 10⁻¹⁸ Hz, far below the reach of current PTAs. This frequency regime may be key to understanding supermassive black hole mergers, early-universe inflation, or phase transitions in the cosmos.^{3, 6}

If successfully implemented, this approach could help constrain models of cosmic inflation, test predictions about cosmic strings, and offer clues about the fundamental structure of spacetime. It may also shed light on the turnover frequency of massive black hole binary populations, an important unknown in cosmology.^{3, 6}

As gravitational wave astronomy matures, diverse detection methods are crucial for confidence in results. Astrometric detection can act as a robust, independent check on PTA findings and provide new constraints on theoretical models, particularly if the signals agree in frequency and direction.⁷

Future Directions

Gravitational wave science is entering a phase of diversification. No single technique can cover the entire spectrum of gravitational wave phenomena. Darling’s work illustrates the value of creative strategies in expanding our observational reach.

While promising, the VLBI-based method faces limitations. Noise and systematics in current astrometric catalogs, especially Gaia, still obscure weak signals. Improving calibration and increasing temporal baselines will be crucial to lowering detection thresholds.⁸

Future projects like the Square Kilometre Array (SKA), next-generation PTAs, and ESA’s Laser Interferometer Space Antenna (LISA) will enhance our ability to explore different frequency bands. Cross-correlating VLBI, PTA, and future space-based data could provide the most complete picture yet of the gravitational wave background, and of the universe's hidden dynamics.⁸

References and Further Studies

Christensen, N., Stochastic Gravitational Wave Backgrounds. Reports on Progress in Physics 2018, 82, 016903.

1. Thorne, K. S., Gravitational Waves. arXiv preprint gr-qc/9506086 1995.
2. Darling, J., A New Approach to the Low-Frequency Stochastic Gravitational-Wave Background: Constraints from Quasars and the Astrometric Hellings–Downs Curve. The Astrophysical Journal Letters 2025, 982, L46.
3. Klioner, S. A.; Lindegren, L.; Mignard, F.; Hernández, J.; Ramos-Lerate, M.; Bastian, U.; Biermann, M.; Bombrun, A.; De Torres, A.; Gerlach, E., Gaia Early Data Release 3-the Celestial Reference Frame (Gaia-Crf3). Astronomy & Astrophysics 2022, 667, A148.
4. Bailes, M., et al., Gravitational-Wave Physics and Astronomy in the 2020s and 2030s. Nature Reviews Physics 2021, 3, 344-366 DOI: 10.1038/s42254-021-00303-8.
5. Lindegren, L.; Klioner, S.; Hernández, J.; Bombrun, A.; Ramos-Lerate, M.; Steidelmüller, H.; Bastian, U.; Biermann, M.; de Torres, A.; Gerlach, E., Gaia Early Data Release 3-the Astrometric Solution. Astronomy & Astrophysics 2021, 649, A2.
6. Sathyaprakash, B. S.; Schutz, B. F., Physics, Astrophysics and Cosmology with Gravitational Waves. Living Reviews in Relativity 2009, 12, 2 DOI: 10.12942/lrr-2009-2.
7. Caprini, C.; Figueroa, D. G., Cosmological Backgrounds of Gravitational Waves. Classical and Quantum Gravity 2018, 35, 163001 DOI: 10.1088/1361-6382/aac608.

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